"Taking into account what happened at the end of the match, Sporting's management has decided to initiate disciplinary proceedings against Bojinov," the club said in a statement after Thursday's 1-1 home Cup draw with lower-tier side Moreirense.
After the penalty was awarded, Bojinov held the ball with one hand and with the other pushed team-mate Matias Fernandez, Sporting's usual penalty-taker, when the Chilean asked him for the ball.
Sporting fans immediately booed and Bojinov's decisive spot-kick was saved.
The 25-year-old arrived at Sporting in the close-season from Serie A's Parma but has rarely featured as he struggles to compete with Dutch striker Ricky van Wolfswinkel and Peruvian Andre Carrillo.
"I was a bit confused about what was going on," grinning Moreirense goalkeeper Ricardo Ribeiro told reporters. "I saw some pushing and shoving and then things calmed down. But that increased the pressure on Bojinov and gave me an opportunity to shine."
