Manchester United midfielder Schweinsteiger faces several weeks on the sidelines after partially tearing ligaments in his right knee earlier this week. He had also damaged the same knee several months ago.
The 2014 World Cup winners take on England on Saturday and Italy three days later in their international friendlies as they prepare for the June 10-July 10 tournament in France.
"It is bitter for him and it is bitter for us," said Mueller, a former long-time team mate at Bayern Munich. "But for the Euro there is still time."
"I cannot estimate exactly how long he will need but it is still possible that he will be at the Euros and it is important for the captain to be there."
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Germany, drawn in Group C, play their first game against Ukraine on June 12. They also face Northern Ireland and Poland in their group.
"Whether it is in the first game and or later, it is important for Bastian to be there. Don't forget it was like that before the World Cup with an injury concern but it worked out very positively in the end."
Mueller also had reassuring words for Mario Goetze, who has been languishing on the bench at Bayern despite having recovered from an injury but blossoms when playing for Germany.
Goetze had scored the winner over Argentina in their 2014 World Cup final victory but has been struggling for match practice under Bayern coach Pep Guardiola.
"As a footballer you cannot live off your past accomplishments and you have to live for the next game and prove yourself every time. Mario was out for a long time injured but he has always had that quality," Mueller said.
"At Bayern he is also in good form in training. But only 11 can play and at Bayern we have seven players for three and a half positions so the situation is not that easy."
"He is back from a long injury break but I want him to play here two good matches, maybe score a goal and put it all behind him."
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
