Giggs scored one of the most memorable goals ever in the competition's long history when he weaved his way through Arsenal's defence in extra time to deliver a knockout blow in a semi-final replay at Villa Park.
Arsenal's Dennis Bergkamp had missed a penalty in the last minute of normal time with the score 1-1.
United went on to complete a treble but Wenger says that night at Villa Park proved pivotal and believes had Bergkamp not missed a penalty, United's run to glory would have been derailed.
"I saw the goal again when Giggs retired," Wenger said in an interview with The Sun. "It won them the treble because if Bergkamp had scored it was game over.
"It was a trauma for us in a negative way and for them in a positive way. It put them on the road to glory.
"I still can hear the shouts of that team having won (2-1). They couldn't believe it, because they were down to 10 men."
Back then Arsenal and United were the two dominant teams in England -- vying for supremacy on an annual basis.
United ended up winning the Premier League in 1999 by a point from the Gunners and completed the treble with an extraordinary comeback against Bayern Munich at the Nou Camp.
"1999 was a miracle year for them," said Wenger, whose side beat United in the 2005 FA Cup final.
With United and Arsenal effectively out of the title race and in the bunch of clubs chasing a top-four finish, Monday's Cup tie offers a welcome distraction from worrying about points.
"The FA Cup is about giving it all on the day," said Wenger, whose side are third in the table, a point above United.
(Reporting by Martyn Herman; Editing by Ian Chadband)
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