"Notwithstanding and without prejudice to the ongoing criminal investigation, it is our view that the player's conduct, in not only bringing the name of Oldham Athletic but also the Football authorities into disrepute, amounts to very serious breaches of club discipline, and therefore constitutes gross misconduct," Oldham said in a statement on Monday.
"Oldham Athletic take matters such as this extremely seriously and believe it was essential to act as swiftly as possible in conjunction with our legal advisers to investigate and deal with this matter decisively once they became aware of the allegations and irrespective of any other investigations and proceedings by other agencies."
British media reported the investigation was centred on lower league matches.
Colombian Montana, 22, scored four goals in 48 appearance for Oldham after joining last year from Premier League side West Ham United, where he started as a trainee but left without making a first team appearance.
Director Barry Owen told BBC Radio Manchester that it had been a very difficult week for the club.
"It's not an easy decision that we've had to make, but it's been made," he said.
"We've got to move on. We've got a big FA Cup tie.
"We've made the decision and we believe that's the right decision for our fans and the football club. I just hope that people realise we've acted positively, and not hastily may I add."
The NCA also charged two players from an English sixth tier semi-professional team and two Singapore nationals earlier this month with conspiracy to defraud contrary to common law.
Oldham are 16th in the 24-team division and face a second round FA Cup replay at fourth tier Mansfield Town on Tuesday with the winners taking on seven-times champions Liverpool in the next round.
(Writing by Patrick Johnston; Editing by Peter Rutherford)
