The hip-hop star, real name Anthony Criss, allegedly failed to stop for police when signalled to in Union City and raced off at high speed before he was detained by officers.
Hours later, he appeared in Central Judicial Processing court in Jersey City, where his bail was set at $15,000 (£9,375).
However, the 43-year-old rapper was also found to have fallen behind on child support and was ordered to settle that debt in Passaic County before he could be released.
Details about the child support order have not been revealed, but Treach is only known to have one child, a 15-year-old daughter named Egypt, with Salt-n-Pepa star Sandra Denton, who he divorced in 2001.
Treach's lawyer, Darryl Smith, has declined to comment on the arrest.