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DeMarcus Cousins is facing a major obstacle in his domestic violence case -- he just underwent knee surgery and is unable to fly to Alabama to turn himself into police, TMZ Sports has learned.

As we previously reported, the Mobile Police Dept. confirmed a warrant was issued for the NBA star's arrest stemming from a threatening phone call Cousins allegedly made to the mother of his child.

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We're told Cousins wants to cooperate with law enforcement but the issue is that he just underwent surgery to repair the torn ACL in his left knee on Wednesday and he's not cleared to fly yet.

It's unclear where the procedure took place, but we're told it was definitely NOT in Alabama. Most doctors recommend not flying for days (and sometimes weeks) after an ACL surgery because of the risks of clotting.

Cousins is facing a 3rd-degree misdemeanor for harassing communications which carries a sentence of up to 1 year behind bars.

We're told Cousins plans on reaching out to law enforcement to come up with a reasonable solution so he doesn't get in trouble.

Cousins tore his ACL during a workout in Las Vegas just weeks after he signed a new contract with the Los Angeles Lakers.

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We broke the story ... Boogie's baby mama Christy West claims Cousins threatened to "put a bullet in your f**king head" when she declined his request to let their 7-year-old child attend his wedding in Atlanta.