Nash said Dragic "doesn't feel well. But that's all I know."
Dragic was placed in the NBA's health and safety protocols.
The loss of Dragic, who is averaging 7.5 points and 4.1 assists, left the Nets' backcourt thin in a 122-115 loss to the Hawks. Starting shooting guard Seth Curry was held out with a sore left ankle.
Nash said another usual starter, forward Bruce Brown has the flu, and also was held out. Nash said he hopes Brown can return when Brooklyn plays Houston on Tuesday.
"I think some of these things are 24 hours to 72 hours,'' Nash said of Brown's illness. "Hopefully, we're in that timeframe and he can play on Tuesday.''
The Nets and Hawks entered the game with identical 40-37 records, with the Hawks now moved up one spot within the projected play-in tournament field to eighth in the Eastern Conference standings.
Meanwhile, Nets forward Ben Simmons is with the team and participated in some light shooting before the game. Simmons apparently is not close to making his debut with Brooklyn since his trade from Philadelphia on Feb. 10.
"He's on the court a little bit the past couple days, but nothing dynamic,'' Nash said, adding Simmons "is not even moving around a lot. He's just doing some light shooting."
The Associated Press contributed to this report.