Ferrari raced in Sunday's Bahrain Grand Prix with a black mark of respect on the noses of their cars following the death of Pope John Paul II.
Schumacher (centre right) meets the Pope earlier this year
World champion Michael Schumacher, who met the Pope with his Ferrari team in January, said he was "very sad".
Schumacher said: "The atmosphere is very strange for all of us. Germans and Italians feel very connected to the Pope, as many other countries do."
As is traditional, all sport in Italy has been called off this weekend.
The live broadcast of the Bahrain Grand Prix was also cancelled, and celebrations at the end of the race were muted.
Race winner Fernando Alonso, from Spain, said: "I think it is a sad day for all of us."
Italian Toyota driver Jarno Trulli, who finished second, raced with a sticker on his helmet saying: "Thank you, Pope."
Trulli said: "Even if it was a great day for me, for the team, for
everybody here, our thoughts and our prayers are towards our Pope who has been teaching all of us a lot of things.
"He has been very close to our religion, he has been travelling all around the world and has been the greatest person I have seen so far.
"That is the reason why we did not celebrate on the podium. We all agreed that it was not the case this time."
The pontiff met the Ferrari team twice - the first time when he visited the team's headquarters in 1988 and rode in a Ferrari instead of his famous "popemobile".
"The Holy Father reaffirmed the importance of sport in the education of the young," Ferrari said in a statement.
John Paul II was an avid sportsman. He played football as a goalkeeper in his youth, and enjoyed hiking, skiing and kayaking.