The Madness frontman is said to have drunkenly made his way to the stage while Sting was performing, and wouldn't leave.
Sting was performing his Police hit 'De Do Do Do De Da Da Da' in front of a packed crowd at Oxfordshire's Henley Festival on Wednesday (July 4).
Suggs then appeared on stage during the song and told the crowd: "I mean this so sincerely. When I was a kid, right, I used to look at Sting and I used to think, one day goddammit. Given the chance.
"And here it is right before you. Ladies and gentlemen, Sting."
Sting replied: "Thank you Suggs, give him a round of applause ladies and gentlemen."
However, the Madness singer did not leave the stage, and continued to dance behind Sting before hugging him.
Three security men had to come on stage to remove him in front of the 6,000-strong crowd.
Watch the incident below (courtesy of The Sun):
One onlooker said: "It was an upmarket black tie event, it was the last place you'd expect to see an ageing rocker drunkenly burst on to the stage."
However, Suggs's wife Bette Bright denied that he was drunk when he stepped on stage, saying: "I wasn't with him. But he wasn't really drunk because he knew he had to go to Stuttgart today.
"He just got on stage, which he always does, and said how much he loved Sting. That was about it. I don't think he was dragged off by security. It's just been wildly exaggerated."
Suggs performed on top of Buckingham Palace with Madness as part of the recent Diamond Jubilee gig.
Madness will embark on a UK winter tour from November.