Alfredsson, who won 11 tournaments on the Ladies European Tour before retiring in September, is understood to have made reference to the helicopter crash which occurred in Glasgow last Friday, killing nine people.
As a noisy helicopter passed overhead during the Omega Dubai Ladies Masters, she told viewers she 'hoped they are better pilots than they are in Scotland'.
The tournament coverage was broadcast on Sky Sports and Scottish presenter David Livingstone quickly apologised.
The 48-year-old Swede later issued a statement via the Ladies European Tour which read: "Regretfully I made an inappropriate and distasteful comment on air today and apologise unreservedly for any offence that was caused by this mistake.
"I did not intend to hurt anybody and I am devastated if I have hurt anyone. I feel very embarrassed because this was not intended in any shape or form."
LET chief executive officer Ivan Khodabakhsh added: "Helen Alfredsson's comment on air was clearly careless but people who know Helen will realise that she would never have intended to hurt someone and I do not believe this was the case."
A spokesperson for the LET later confirmed that Alfredsson would not commentate on the remaining two days of the tournament.
Although Alfredsson was not working directly for them, broadcaster Sky Sports said they were "shocked" by the comments and also issued an apology.
A statement from Sky Sports read: "Sky Sports offered coverage of the Dubai Ladies Masters tournament on Thursday with live pictures and commentary provided by a world feed broadcaster, supported by presentation from our own studios in London.
"Sky has no control over the commentary from the event, which is shared by a number of international broadcasters, and we were shocked at the unacceptable comments made by one of the analysts.
"As soon as coverage switched back to our studio in London, our presenter David Livingstone apologised and we reiterate our apology for the offence caused by these comments. We have also expressed our strong concerns to the world feed broadcaster."
Alfredsson's comment came only days after Katie Hopkins had to retract a tweet on Scottish life expectancy, made just after the Clutha crash.