Nets coach Avery Johnson characterized Wallace's status as day to day.
"He's just gonna continue to get treatment on his ankle," Johnson said. "Obviously, his X-rays were negative, and that was great. So (trainer) Tim (Walsh) is gonna continue to treat him. He's feeling a little bit better, but not good enough to play tonight."
It is not known whether Wallace will be ready for Wednesday night's game against the Miami Heat.
"What we're hoping for is he gets well, and when he's ready to come back, we'll get him back out there," Johnson said, then joked, " ... so (Bogans) will go from being an inbounder at the end of the game (Saturday) to the starting lineup. Isn't that amazing?"
Bogans has started 310 games in his career, including a career-high 82 with the Chicago Bulls in 2010-11. He started once for the Nets last season.
Johnson said Bogans, who was dealing with knee and tailbone injuries during the preseason, will be on a minutes limit.
"I don't think I can take him to 24 minutes," Johnson said.
Wallace landed on Lowry's foot and came down awkwardly. He tried to remain in the game but limped off the court and into the locker room, then received X-rays.
In 30 minutes Saturday, Wallace had 10 points, 6 rebounds and 4 assists. The Nets will miss his versatility, especially on defense, where he can guard multiple positions.
Johnson, who called Wallace "irreplaceable," said he elected to start Bogans so as not to disrupt his rotation, which features C.J. Watson, MarShon Brooks, Reggie Evans and Andray Blatche coming off the bench.
Johnson also announced that reserve small forward Josh Childress will miss his second straight game due to a sprained left ankle.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.