The former Conservative chairman, who was injured along with his wife during the 1984 IRA bombing of the Grand Hotel in Brighton, said he hoped Mr McGuinness was shot in the back for attending a state banquet at the invitation of the Queen.
Mr Adams said it was unacceptable for a member of the House of the Lords to openly support the shooting of a political leader.
"I fully understand that Norman Tebbit has himself been a victim of the political conflict and I regret that he has suffered grievously," said Mr Adams, a former West Belfast MP and now TD for Louth in the Irish parliament.
"However, to publicly advocate the assassination of Deputy First Minister Martin McGuinness is a shocking throwback to a violent past from which we are seeking to move on."
Mr Adams said his party colleague and ex-IRA commander Mr McGuinness has worked tirelessly to ensure the success of the peace process at considerable risk to himself.
"Political leaders on both sides of the Irish Sea should reject the sentiments expressed by Mr Tebbitt."
Mr McGuinness said: "Obviously the sentiments that he has expressed, I think, are not fitting for someone in the elected position he has been in for a very long time."
Lord Tebbit said the Queen had no choice about Mr McGuinness attending the state banquet at Windsor Castle on Tuesday night in honour of the historic visit of Irish President Michael D Higgins.