Pratt was dining with his The Hills co-star and fiancee Heidi Montag when the incident at the Beverly Hills Hotel occurred.
Pratt claims Madden was angry about comments he was incorrectly reported to have made about Richie's weight.
He tells website In Touch Online, "I was sitting having a quiet lunch with Heidi when Nicole walked in and started pointing at me and then whispering to Joel.
"He storms over and starts shouting, 'You've been talking s**t about my girl.' I told him, 'Please can we not do this at the Beverly Hills Hotel. This is ridiculous.' Then he started screaming and calling me names."
At this point, Madden and Richie were asked to leave the hotel.
Pratt adds, "It all stems from an interview in (American magazine) Details ages ago where I was misquoted calling Nicole a skinny bitch. It's all a misunderstanding. I've always thought she's a really nice girl and I wouldn't call her that."
Source: WENN