He will not play Sunday at Rider and will also miss Friday's home game against Saint Peter's.
"We hold our student-athletes to a higher standard than was displayed last night," Iona coach Tim Cluess said in a statement. "We should know and will use better judgment in the future, regardless of provocation."
A source with direct knowledge of the situation told ESPN's Andy Katz that MAAC commission Rich Ensor is likely leaning toward a reprimand for Iona's and Monmouth's coaching staffs for their pre- and postgame behavior. But the situation remains fluid, as videotape and statements are being reviewed.
Tempers flared on both sides after Monmouth's 110-102 victory in New Rochelle, New York, on Friday, as Gaels and Hawks players tussled while going through the postgame handshake line.
It wasn't immediately clear who sparked the altercation, which included Washington slapping Monmouth's Chris Brady in the face. Coaches and security attempted to calm the situation before the teams finally exited Hynes Center Court.
"Chris' nose is about this swollen right now, so if [Washington] slapped Chris that hard, man he should maybe try MMA because nobody smacks, and the kid's nose is this big downstairs right now," Monmouth coach King Rice told reporters after the game. "So I don't know if it was a smack or what it was, but big Brady's nose is pretty messed up right now."
Monmouth has drawn headlines this season for its eccentric bench celebrations; in the lead-up to Friday night's game, Cluess was a harsh critic of the bench mob, critiquing its over-the-top actions.
"Are they on the team?" he said earlier Friday. "I didn't know if they were on the team or wearing uniforms as cheerleaders. I've never seen them on the court doing anything, so to me, they're not basketball players."
The teams play again Feb. 19.
Information from ESPN's Andy Katz was used in this report.