The man detained by police was Matthew Brooks, 22, a probationary constable with West Mercia police.
The arrest came after Brooks and schoolgirl Naomi Mills were found in the north of Scotland on Monday night after an extensive search.
Moments before the arrest was announced two plain-clothed police officers were seen leading a man from a hospital in Wick.
A police spokesman said: “At 3.30pm today a man was arrested on suspicion of the abduction of a 15-year-old girl.
“That man will be interviewed by officers from West Mercia Police in due course.”
The parents of Naomi spoke yesterday of their relief that their daughter and had been found safe.
Bev and Mel Mills said in a statement issued by West Mercia Police: “We are very relieved and grateful that they have been found safe and well and we would like to thank everyone involved.
“We are looking forward to be able to see Naomi again for the first time since Friday and our thoughts are with Matthew’s parents.”
The teenager’s parents added: “We’re so grateful to both officers from West Mercia Constabulary and the Northern Constabulary for doing such a fantastic job.”
Naomi and Mr Brooks were found by a police dog handler while walking in a wood near Tongue in northern Scotland on Monday night. They were found at about 7.40pm, three miles south of Tongue, near to where their car was found on Sunday morning.
Naomi left her home in Worcester four days ago to walk to Chantry High School, Martley, Worcestershire, but never arrived.
Mr Brooks failed to turn up for work on Friday night and had not been seen since that morning.
Police were alerted after the couple were spotted by a reporter who passed them in his car.
Before Pc Brooks’ arrest, his parents also spoke of their relief at the news that the couple had been found.
Elizabeth Brooks released a statement through police on behalf of herself, her daughter and Pc Brooks’ grandparents. She said: “We were so relieved and pleased that Naomi and Matthew have been found safe and well and we are very grateful for everybody’s help in finding them.”
Adrian Brooks, Matthew’s father, who is estranged from Mrs Brooks, said: “We are extremely grateful for the successful outcome to this incident and sincere thanks go out to West Mercia Police and the Northern Constabulary.”
Mr Brooks, a long-serving police officer who is also stationed in Worcester, added: “We would ask that the family’s privacy is respected and that we will be giving no other statements and interviews.”
Journalist David Ross, who alerted police after spotting the couple, yesterday described his role in helping end the massive search.
Mr Ross, said he was driving home along the road to Altnaharra in the evening and was amused to see two people matching their description walking “intertwined” ahead of hi m about four miles from Tongue.
“I passed them and looked in the mirror,” he said.
“They appeared completely unperturbed, engrossed in each other as they walked intertwined on the road.”