The 30-year-old Bayern Munich goalkeeper withdrew because he felt unwell shortly before Germany's flight to Rimini.
The 30-year-old Bayern Munich goalkeeper withdrew because he felt unwell shortly before Germany's flight to Rimini to face the microstate in northern Italy.
He will also miss next Tuesday's friendly against Italy in Milan in Germany's last international of 2016.
In Neuer's absence, Barcelona's Marc Andre ter-Stegen and Bayer Leverkusen's Bernd Leno will take over in the Germany goal.
Neuer is the latest first-choice star to drop out alongside Real Madrid's Toni Kroos, who has a fractured foot, and Bayern team-mate Jerome Boateng, who is out with an injured knee and groin.
Arsenal's Mesut Ozil has been rested while winger Julian Brandt pulled out on Wednesday with an intestinal disorder. Attacking midfielder Julian Draxler is also injured.
Despite the withdrawals, Germany's head coach Joachim Loew expects his side to take the three points to remain top of their qualifying group with four wins from their first four qualifiers.
"We will treat the last qualification game of the year exactly the same as the three previous games," said Loew after Germany's wins over Norway, the Czech Republic and Northern Ireland in the last two months.
"We don't want to be arrogant in San Marino and will treat this with high levels of concentration and seriousness."