Newly elected leader Mary Lou McDonald told members to “think of what you retweet” as she called on elected officials to also apologise promptly when at fault.
Senator Máire Devine had retweeted an offensive tweet relating to Brian Stack, an officer in Portlaoise shot in the neck by the IRA in 1983 and who died later.
Ms Devine apologised over the retweet and said it was never her intention to cause distress or hurt.
She said: “It was never my intention to cause any distress or hurt, particularly to victims of the conflict. I want to offer my most sincere apologies to the family of the late Brian Stack.”
Austin Stack, son of the slain officer, had called for her resignation and said the senator was “revictimising” him.
A retweet by Ms Devine had referred to Mr Stack as the “Fianna Fáil son of a sadist prison officer”.
The retweet has since been deleted from the senator’s Twitter account.
Sinn Féin said it “strongly disapproves of what has happened. There can be no excuse for the hurt and offence which has been caused to the Stack family.”
The incident represented “unacceptable behaviour” on the part of an elected representative, said Declan Kearney, national chairman of the party.
Ms McDonald said she had “zero tolerance” for actions that bring grief to families, as she apologised to the Stack family.
Ms Devine understood she had made a “catastrophic error of judgment”, and her biggest mistake was not deleting the retweet immediately and apologising, said Ms McDonald.
Ms Devine will be banned from all party activities for three months and will be outside Leinster House for that time.
Mr Stack, who has campaigned for his father’s murderer to be brought to justice, called the tweet “disgusting”.
He said Sinn Féin must go further and expel Ms Devine.