Botha wanted to join his Springbok partner and Bulls captain Victor Matfield at French outfit Toulon.
But the club felt it had to make a stand with Matfield unlikely to be released by Toulon to play Super 14 rugby as had been hoped.
"We had no option to decline his (Botha's) request," said Bulls commercial manager Ian Schwartz.
"We have invested in him and his contract was last year renewed for a further five years. Releasing him would send a message to other players that contracts are not binding which in turn could conceivably lead to an exodus."
Botha's chances of playing in the Super 14 opener against the Stormers on Saturday are slim as he remains hampered by an ankle injury.
However, Danie Rossouw has recovered from a neck injury so he and Wilhelm Steenkamp will fill the void left by Botha and Matfield.
Tighthead prop Rayno Gerber also returned to training on Monday and should be available to face the Stormers.