The former Germany and Bayern Munich captain fell out of favour at Old Trafford when Jose Mourinho deemed him surplus to requirements after taking over as manager in the summer.
Ibrahimovic told Sky Sports News: "I'm happy for him. I'm happy because the situation for him hasn't been easy.
"He has been working hard, he's kept patient and mentally it's not easy - especially when you have had a career just like his. I have nothing but respect for him and super happy that he's back.
"And also the person is fantastic, so happy to see him back on the field and you could see the crowd was happy also."
Schweinsteiger continues to be linked with a move away from United in January, with Brazilian club Santos reportedly interested in the World Cup winner.