Rooney's 273rd goal for the club puts him level in second with Denis Law on United's all time goalscorer list.
And Schweinsteiger believes that strike will give his team-mate confidence to add more to his goal tally.
"We are just happy that we could finish one of our attacks," he told the club's website.
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Wayne Rooney celebrates scoring in their 1-0 win over CSKA Moscow
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Bastian Schweinsteiger congratulates Rooney on his goal
"I am also happy for Wayne that he scored his goal and I think it will give him a lot of confidence and I hope he can use this confidence in the next match against West Brom.
“It was a big moment for us because we hadn’t scored a goal in the last few matches so it was very important, especially after the big chance for Moscow in the second half."
A win against PSV Eindhoven in United's next Champions League match will guarantee their progression to the last-16.
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