Kelly is accused of filming himself having sex with a girl believed to have been 13 or 14 at the time.
The famed R&B artist, who is required to get permission for each trip out of Illinois, has pleaded not guilty in the case, which has been pending since 2002.
Judge Vincent Gaughan entered a warrant for Kelly's arrest Wednesday, but it will not go into effect until Thursday when Gaughan ordered Kelly to appear in court, the Chicago Sun-Times reported.
"This is just an abuse of the process. It's disrespectful of your honor," said Assistant State's Attorney Shauna Bolicker. Gaughan replied, "I don't take this lightly, either."
But Kelly's lawyer, Ed Genson, said the singer was "detained because of some snow" while returning from a gig in Sacramento.
State police later pulled Kelly's tour bus over to inspect its log, which details how long an individual has been driving the vehicle.
Police ordered the driver to stop because the log had not been properly filled out, Genson said.