One national newspaper suggested over the weekend that the Hillsborough team’s squad received a maximum of £17,000 of their pay cheques last month and were told the rest would be delayed.
The report went on to claim the Championship club settled the outstanding amount days later.
But speaking after the Owls' 1-1 draw at Derby County, Monk denied the claim.
Describing it as a “nonsensical story”, he told The Star: “I can tell you all the players are fine.
“Everyone has been paid.
“It is absolutely a non-starter."
Wednesday, who sit in eighth position, one point shy of the play-off positions, are currently embroiled in a row with the English Football League over the legality of the sale of Hillsborough to owner Dejphon Chansiri.
If the Owls are found guilty by an independent disciplinary commission of breaching the governing body’s Profitability and Sustainability rules, they could be hit with a possible points deduction, anything between 12 and 21 points.
P&S rules state clubs are only allowed to lose £39m over a three-year period.
Wednesday argue the EFL charges are “unlawful”, insisting the league agreed to the stadium sale and including the cash in their 2017/18 accounts.
Monk, whose former club Birmingham City were docked nine points for falling foul of P&S regulations last season, said: "I’ve got experience of it at Birmingham.
“There’s no excuse for us, players or manager.
“I understand fans will be worried and players will talk about it.
“But I’ve spoken to them (the players) from experience.
“It doesn’t directly affect what we can do in training or a match.
"The club has made a statement and I think it is clear to see that the club feels it has done everything right and we have no reason not to believe that.
“We support that and we are here to fight for this club and do our part of it, which is the football side of it.
“We are here fully supporting each other.”