The Switzerland international completed his switch to San Siro from German champions Bayern Munich on a four-and-a-half year contract on Friday.
Shaqiri has not featured in competitive action since December 16, though, due to the Bundesliga's mid-season break.
And head coach Mancini will only use the winger sparingly against Genoa.
"I don't think Xherdan Shaqiri is ready to play 45 minutes or even 30," he said. "He hasn't played since December."
Shaqiri's signing followed the arrival of forward Lukas Podolski on loan from Arsenal earlier in the week.
Mancini believes the challenge of helping restore Inter's standing among the best teams in Europe convinced the pair to join.
"There are few clubs as big as Inter," Mancini added. "We have a big appeal. We have had difficulty, but the new arrivals can help us get back to the top."
The Italian also confirmed that Nemanja Vidic will play against Genoa despite not being fully fit as Inter's options in defence are limited due to a four-match ban for Juan Jesus.
