Bradford have fined Stuart McCall and Andy Myers the maximum of two weeks' wages following their on-field altercation at Elland Road on Sunday.
City captain McCall was punched in the face by Myers during the club's 6-1 derby defeat against Leeds, and needed stitches in a gash under his eye.
Club chairman Geoffrey Richmond described the incident as his "most embarrassing moment in football".
And a statement on the club's official website, www.bradfordcityfc.co.uk, read: "Following due consideration of the incident at Elland Road on Sunday where Stuart McCall and Andy Myers were involved in an altercation just before half-time, it has been deemed by manager Jim Jefferies and chairman Geoffrey Richmond that both players be fined the maximum two weeks' wages.
"The club wishes to make it clear that such behaviour is totally unacceptable and will not be tolerated."
Richmond told a local Yorkshire newspaper: "From my point of view, their actions were unforgiveable, and I feel ashamed.
"It was awful, my most embarrassing moment in football, and I wouldn't ever want to see Bradford City players behaving like that ever again." - PA