Griffiths has been charged by police for “culpable and reckless conduct” after being accused of kicking a smoke bomb into a stand housing St Johnstone fans during Wednesday’s Premier Sports Cup quarter-final at Dens Park.
Griffiths is also likely to feel the wrath of the SFA, with the forward expected to be hit with a ban.
However, he is free to play Rangers on Saturday and McPake is not worried about the Scotland internationalist facing the Ibrox club, with the loanee yet to score in his second spell on Tayside.
“I have absolutely no concerns about playing Leigh against Rangers, Hearts, whoever it is,” Dundee manager McPake said.
“I know Leigh as a character and he’ll handle the occasion.”
Griffiths has missed opportunities in the three games he has played since completing his move to Dundee, but McPake believes he can break his duck against the reigning cinch Premiership champions.
“I’m hoping that it is [the match he scores in], and that we create the chances,” he said.
“If we keep creating those clear-cut chances and if they fall to Leigh then there’ll be goals.”
Dundee currently prop up the division, but McPake feels his team’s displays have not mirrored results.
"We’re winless but performances have been good,” McPake continued. “I question myself at times if I keep coming out and saying that but it’s the truth. Anyone that’s watching back can see the clear-cut chances we’re making.
“There may not be as many tomorrow because we’re playing a Rangers team who are the champions. Steven Gerrard has made them a formidable outfit, to say the least.
“We’ve got to have a game plan. We want these games and that’s the reason we wanted back in the Premiership, for Rangers and Celtic coming here and the derbies. Of course we’re exited but we need to have a game plan and we need to stick to it.
“The fans will be behind us, there’s no question about that. Regardless of whether you’ve won none in ten or ten out of ten games.”