A man in his 40s has been arrested and is being held at Castlerea Garda Station.
It is understood that Mr Horkan was shot with his own weapon during a scuffle with a man close to the Garda station.
It is believed the officer had intervened in an incident unfolding on the street as he was returning to the station.
"My thoughts, and the thoughts of all personnel in An Garda Síochána, are with the family, friends and colleagues of Detective Garda Colm Horkan at Castlerea Garda Station and the Detective Unit he served in," Mr Harris said.
"Colm served the communities he worked in with distinction and pride during his 24 years as a member of An Garda Síochána.
"Detective Garda Colm Horkan is the 89th member of An Garda Síochána killed in the line of duty. Today is a terrible reminder of the significant sacrifices, including the ultimate sacrifice, that Gardaí make to keep people safe.
I want to thank the local community in Castlerea and the country as a whole for the support they have shown to An Garda Síochána and individual Gardaí even in the short time since the incident.
"The fatal shooting of Detective Garda Colm Horkan remains under investigation. I want to appeal to anyone with information on this incident or witnessed this incident to contact Castlerea Garda Station at 094 962 1635.”
Detective Garda Colm Horkan.— Garda Info (@gardainfo) June 18, 2020
RIP - 17th June 2020.
Ar dheis Dé go raibh a anam. pic.twitter.com/O1MHMHMB2L
AGSI General Secretary Antoinette Cunningham added: "We are all very devastated. It is absolutely devastating news.
“There is somebody in custody, so we have to be very careful of what we say.
But a Garda has lost his life in an incident on duty and that is all we can think about this morning.
"Our thoughts go to his family and friends and colleagues in Roscommon at this time.
“I spoke to the chief superintendent up there this morning and they are all absolutely devastated at his loss.
"It's very, very tough."
GRA President Jim Mulligan said Det Garda Horkan was a popular member of the force.
"He was a member of Charlestown GAA and played underage football for his native county.
"He was always regarded as a go-to man in Charlestown GAA. Nothing was too big or too small a request for him.
“Colm was a gentleman known for his kindness and commitment to helping other people. He died protecting his community and serving his country.
“Our thoughts are with Colm's family, colleagues and the communities he served at this very distressing and traumatic time."
The Policing Authority chairman Bob Collins described news of the death as a "shock".
“The Policing Authority has learned with great shock and dismay of the death of a Garda in Co Roscommon," he said.
“The killing of a Garda, as well as being a wilful denial of the right to life, is an attack on the essence and the foundations of our democracy.
“It is a fundamental assault on the principle of equality. In the midst of exemplary service to the community during the health emergency, the Garda Síochána will mourn the death of a colleague.
“On behalf of the Authority, I extend deepest sympathies to the family of the Garda and to his colleagues throughout the organisation.”
Locals TDs, Taoiseach Leo Varadkar, Justice Minister Charlie Flanagan as well as politicians from other parties
"I extend my deepest sympathies to the family and friends of the Garda who has died in the course of their duties," Mr Varadkar said of the guard who joined the force in the mid-1990s.
"Every day our gardaí put themselves on the frontline of crime prevention, on behalf of all of us. This requires regular acts of bravery and courage.
Sometimes the outcome is tragic and a Garda makes the ultimate sacrifice in the course of their duties.
Minister for Justice Charlie Flanagan added that a full murder investigation is underway.
“The brave Detective Garda who died last night died in the line of duty, serving and protecting the community. His death will cause untold heartbreak to his family, loved ones and all his colleagues in An Garda Síochána across the whole country," he said.
President Michael D Higgins said: “The death of a Garda detective on duty in Castlerea has come as a shock to us all.
“As President of Ireland I wish to express my deepest sympathy to the family and friends of the Garda, and to all those who have been affected by this tragedy.
“An Garda Siochana play a crucial role in our communities and this loss of life is traumatic for our society as a whole.
“I have contacted the Garda Commissioner to express my deepest sympathies on this terrible loss of a member of the force.”
Sinn Féin’s Mary Lou McDonald said it’s a sad and difficult day for gardaí.
North of the border, Police Service of Northern Ireland Chief Constable Simon Byrne offered his condolences.
“Awful news this morning coming... with the death of a Garda colleague in Castlerea,” he tweeted.
“Thoughts from all [the PSNI are] with his family, friends and colleagues at such a difficult time.”
Local TD Frank Feighan expressed his horror at the shooting saying people in the town are “shocked and sad” this morning.
“This man was killed in the line of duty, shielding us from harm and protecting the vulnerable and it is a terrible price to pay,” he told.
Independent TD for Roscommon Denis Naughten has described the shooting of a detective garda in Castlerea as devastating news for the area.
“This is devastating news for his family, for his fellow gardaí and the community,” Mr Naughten told.
The London Met Police Federation said: “Devastating news from Ireland as a Garda colleague is shot dead. Our thoughts with his family, friends and close colleagues and with all our GRA colleagues.”
Gardaí are appealing for witnesses or anyone with any information to come forward.