The Germany international made his competitive debut for United in Saturday's 1-0 win over Tottenham at Old Trafford, coming on in the final 30 minutes to help build up his fitness after injury during pre-season.
Now the 31-year-old believes he is nearing full fitness - something Pep Guardiola suggested had been eluding him for the past three seasons at Bayern - just in time for United's clash with Brugge on August 18.
"It's fine," he told MUTV when asked about his calf.
"I had three or four days in America where I had this injury and it was not so good for my rhythm. Now I feel much better and also the game was very important to play 30 minutes.
"The training sessions are very important for me, too. I'm getting better and I hope I will be 100 per cent fit in the next week."
Schweinsteiger was given a rapturous applause at Old Trafford when he replaced Michael Carrick in the opening game of the season and the World Cup winner admitted he was overwhelmed by the occasion.
He said: "It was amazing, really. I was surprised and I have to say 'thank you' to all the supporters. It was a great feeling and yes, at the end, we won so it was a good day for us.
"I’d played twice before in the Champions League but this was something new on Saturday.
"The support is huge; I knew that before I came here and saw it in the USA as we had a lot of supporters there too. It was great and a special day for me on Saturday."
