Joaquin Bilbao and his driver spent the night in a police cell. Bilbao denied firing the shots at the door of a brothel, which was closed.
"For personal reasons, for family reasons and, above all, for the good of the club, I have decided to submit my resignation," Bilbao said on RNE radio.
Xerez is in first place with 51 points, two ahead of Hercules and Tenerife.
Altidore has not played for Xerez since moving on loan from Villarreal.