Burks injured a knee during Leopards' 85-70 defeat at London Towers last weekend and has been replaced by Thames Valley Tigers' Jason Siemon in the South team, coached by Mims.
Leopards, league leaders and defending champions, play Watford on Wednesday, then face three testing final games against Derby Storm, Tigers and away to Sheffield Sharks.
Burks played for 37 minutes in Thursday's 81-72 win over Crystal Palace, but will be at tomorrow's game only to sign autographs. Mims said: "Although Eric is disappointed he knows the importance of the league games in our bid to keep the title. The break will give him plenty of time to rest before we play Watford."
Birmingham Bullets must win all six of their remaining games, beginning with tomorrow's All-Star curtain-raiser against Sheffield, to keep the pressure on Leopards.
Defeat last weekend cost Bullets and Sharks the chance to close the gap. Bullets coach Mike Finger said: "I'm sure Sharks aren't very happy right now and neither are we. We're two angry teams both wanting to prove a point."
l Kareem Abdul-Jabbar, the NBA's career leading scorer, was arrested by US Customs officials on Sunday for possession of six grams of marijuana at Pearson International Airport. The Toronto Star said Abdul-Jabbar, 50, the former Los Angeles Lakers centre was fined $500 (pounds 330) before being allowed to board a flight to Los Angeles. He was released without conditions.