The IT Crowd star attended the musician's set at the festival backstage, and was later beckoned over by the singer, real name Ben Drew.
"I'm certainly not at that level of fame where I get mobbed or even recognised all the time," he told the Daily Mail.
"This summer, I was backstage at Glastonbury waiting for rapper Plan B to perform. I'm a bit of a fan and we had eye contact for a second. He nodded to me to come over, and I thought: 'Great, he knows who I am'.
"He said: 'Hey, man, could I get some water?' He had no idea who I was. And I felt obliged to get him the water."
O'Dowd also revealed how he proposed to fiancée Dawn Porter in Guernsey, where the TV journalist grew up. The pair announced their engagement in December.
"We went for a walk on the beach with her dad and aunt and uncle who brought her up," he explained. "I'd been traditional and asked for their permission. Dawn and I went on ahead and I was trying to pluck up the nerve.
"Then we got to a pretty harbour wall and I asked her to take a picture of me, and she turned around and I was down on one knee with this ring and all of that sort of nonsense. Then we went to the pub where Dawn used to work and celebrated with shepherd's pie and champagne."
The Bridesmaids actor recently said that he hoped a sequel would not be made of the film.
> Chris O'Dowd: 'BAFTA campaign was shameless'