The Red Devils' record signing has been put straight into the starting line-up by David Moyes, who also welcomes back the Dutch striker after a seven-week lay-off
Mata signed from Chelsea for a club record £37.1 million on Saturday, and has been thrown straight into David Moyes' starting line-up.
Van Persie has been out of action since December 10, when he was withdrawn injured against Shakhtar Donetsk in the Champions League.
Wayne Rooney has been named among the substitutes after recovering from a groin injury, and there is no place in the XI for Adnan Januzaj.
Marouane Fellaini is not fit enough to make the squad despite training alongside Rooney and Van Persie on Monday. United's central midfield pairing on Tuesday will be Phil Jones and Ryan Giggs.
Ole Gunnar Solskjaer will return to Old Trafford as the Cardiff manager, and will be hoping to inflict a sixth defeat in seven matches on the Premier League champions.
Manchester United starting line-up in full: De Gea; Rafael, Smalling, Evans, Evra; Valencia, Jones, Giggs, Young; Mata, Van Persie.
Subs: Lindegaard, Cleverley, Fletcher, Januzaj, Kagawa, Hernandez, Rooney.
Cardiff City: Marshall, Caulker, Hudson (c), John, Mcnaughton, Medel, Whitts, Noone, Mutch, Bellamy, Campbell.
Subs: Lewis, Turner, Kim, Eikrem, Gunnarsson, Daehli, Berget.