The motion for continuance was filed with the Eagle County court Tuesday night and made public Wednesday. Bryant's trial for sexual assault was scheduled to begin Aug. 27.
The move followed Tuesday's filing of a civil suit by Bryant's accuser, seeking unspecified monetary damages.
Legal experts are divided on how the civil suit will affect the criminal trial, KUSA said.
Former Denver District Attorney Norm Early said he doesn't believe the civil filing will affect the criminal case.
But, criminal defense attorney David Lane said the civil action "throws an almost insurmountable hurdle into the prosecutor's path."
The Los Angeles Lakers star has denied assaulting the woman and said the two had consensual sex.