Evans was due to present live coverage of the third round of the prestigious golf tournament from 9pm on Saturday. However, the show had to start without the presenter after he turned up 25 minutes late.
After apologising "profusely" for the tardiness, Evans said that he had forgotten what time the programme was due to start.
"I ran in from where I was - well, I did the Augusta shuffle," he said, referring to the venue of the US Masters.
Asked by his co-presenters where he had been, Evans replied: "I've been watching the golf. That's what we came to do.
"I had no idea we started at 9pm. I was in the foyer having a water and a chat."
The breathless presenter had to run up the stairs to the 5 Live studio after being told that he was due to be on air.
He added: "How's it going anyway? I had such a great introduction written and everything. Oh well. I'm here now."
A BBC spokesperson said that Evans's late arrival was down to a "pure misunderstanding" over the scheduled start time of the show.
During his two-year stint as Radio 1's breakfast show host in the mid-1990s, Evans became known for his often erratic time-keeping.
He now presents the breakfast programme on Radio 2, after taking over from Sir Terry Wogan in January last year.