Vice-captain Schweinsteiger returned from a long-term knee injury in November and has been limited to eight appearances in all competitions for the defending Bundesliga champions.
The Germany midfielder scored his first goal of the season in a 2-1 win at Mainz in the final game before the mid-season break in December.
And winger Robben wants Schweinsteiger to get back to his best form as the Bavarians seek to win the treble under Pep Guardiola.
"Basti is one of our captains, that says it all," Robben told Bayern's official website.
"He has a difficult period behind him. I hope now that he can really attack again in January. We need him."
Bayern goalkeeper Manuel Neuer is one of the three finalists for the FIFA Ballon d'Or.
Neuer faces competition for the award from Real Madrid star Cristiano Ronaldo and Barcelona forward Lionel Messi. However, Dutchman Robben feels that Neuer is worthy of the honour.
"I do not know [what Neuer's chances are]," Robben added. "But I can say that it would be deserved for Manu.
"He had a great year. His body language, his strength. If you are standing in front of him as a striker and he makes himself big, that's impressive. I keep my fingers crossed for him."
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