Mourinho insisted Juan Mata, Chelsea's player of the year in the past two seasons, leaves for Old Trafford with the full blessing of everyone at the club after finding chances limited this term.
Wenger suggested the transfer was unfair, as Chelsea have already played United twice this season and will not have to face Mata this term, while other title contenders will.
Mourinho, whose side play Stoke in the FA Cup fourth round on Sunday, turned the Frenchman's criticism against his old adversary, by pointing out Arsenal's favourable fixture list.
"Wenger complaining is normal, because he always does," Mourinho said.
"Normally he should be very happy that Chelsea sold a player like Juan Mata, but this is also a little bit his nature.
"When he says this is not fair, I think what is not fair is that his team always has the best days to play. Always.
"This week, a week without midweek games, what everybody wants to do is to play earlier to have more time to rest for the next week.
"One team plays Friday (Arsenal v Coventry), another one plays Sunday (Chelsea v Stoke). Who plays Friday? Who plays Sunday?
"This is not fair. And when you go to the fixtures during the season, it's never fair, because they always get the right time to rest, the right time to play."
Chelsea are keen to complete a deal for Basle winger Mohamed Salah before Mata's move to United is concluded, but the Spain playmaker goes with Mourinho's best wishes.
World Cup winner Mata last featured at Southampton on New Year's Day, when he showed his frustration after being substituted early in the second half.
"He was clearly affected, disappointed, frustrated, so things went in this direction," Mourinho said.
"He's a fantastic player and despite not playing a lot for us in the last period could be a very important player for us. But Juan had this fantastic opportunity for him.
"It's what he wants. It's what he asked us to accept. Chelsea Football Club is proud to act this way, in an open way, in a human way.
"Everybody in this club, the owner (Roman Abramovich) to the last man, wish him very good.
"We hope he does well, we hope he is happy at United and, for sure, when one day he is back at Stamford Bridge in a United shirt, for sure the stadium will show him how much they want him and how much they respect what he did here."
Some commentators have suggested Mourinho is no longer concerned by Manchester United after selling to a direct rival, who are 14 points adrift of the title race.
Mourinho sees no reason why Chelsea should not sell to United, even though their rivals rebuffed two Blues bids for striker Wayne Rooney last summer.
"To say now 'Juan, you cannot go to United because United refused in the summer to sell us Wayne Rooney' I don't think is fair to Juan and I don't think it's the way for us to act," Mourinho said.
The Portuguese confirmed United have broken their transfer record - a £30.75million deal for Dimitar Berbatov in 2008 - to recruit the 25-year-old and believes David Moyes knows exactly the player he is getting.
Mourinho said: "If Man United pays their record for a player it's because they know exactly what they want.
"It's not a gamble to see if he adapts well or not. They are convinced he is going to be an important player for them."
Mourinho and Chelsea moved quickly to replace Mata with Salah after reaching an agreement with Basle, subject to personal terms and a medical.
Mourinho has spoken to Salah, who was also interesting Liverpool, whose manager Brendan Rodgers has not given up hope - and Mourinho admits a last-minute U-turn is feasible.
"We know that the player wants to come (to Chelsea). He told me personally," the Blues boss said.
"Probably the situation is still open and not closed."
Salah is set to become the third signing of the winter transfer window, following the captures of Bertrand Traore and Nemanja Matic.
Kevin De Bruyne has already left for Wolfsburg, Mata is en route to Manchester and Michael Essien has permission to leave, too.
Striker Fernando Torres (knee) is missing for three weeks and Mourinho is not yet at full fitness following elbow surgery on Monday.
"I can play but I cannot make throw-ins," he said.
"It was an old fracture, but now I was feeling pain and losing mobility in the elbow so we decided to do it now."