Four men in an open-top car attacked Ray Fearon, Chook Sibtain and Lawrence Wood as they were walking outside their hotel in the Gare du Nord area of the city. They punched the actors to the ground.
Fearon, who is black and plays Romeo, was taken to hospital with a sprained hand. Chook, who is of mixed race and plays Mercutio, was the most badly hurt and had 10 stitches for facial wounds. Lawrence Wood, who is white, suffered minor injuries.
All three have recovered from the unprovoked assault, which took place earlier this week, and are continuing to appear in the production.
Belgian police are investigating the incident, which was captured on closed-circuit television. No one has been arrested.
The Royal Shakespeare Company normally provides taxis for performers after shows but the actors had been strolling in their free time, walking back from a restaurant after a meal.
A spokeswoman for the RSC said that the men were shaken but were keen to continue the tour, which now goes to Japan. The company will not be introducing any new security measures.
t The National Theatre actress Charlotte Cornwell is to step down as vice-president of the actors' union Equity after four years. She will not contest the forthcoming Equity council elections because she wants to spend more time on her career. She is currently appearing at the National Theatre in Ibsen's An Enemy Of The People.
Tipped to take her place as union vice-president is Susan Tully, who played Michelle in BBC TV's soap EastEnders. Tony Robinson, who played Baldrick in Blackadder, is the favourite to become union president.