A board with messages wishing the 38-year-old nine-times world champion a speedy recovery was displayed on Rossi's side of the garage at the track near Rossi's home on Italy's eastern Adriatic coast.
"I thought I could go a little bit faster but I did some mistakes on the lap and could not push more than I was," said Vinales, who will share the front row with Ducati's championship leader and home hope Andrea Dovizioso and Honda's Marquez.
It was his fourth career MotoGP pole position and he secured it with a late lap of one minute 32.439 seconds, 0.162 quicker than Dovizioso who had looked set to take the top slot.
Britain's Cal Crutchlow, who this week sliced the index finger on his left hand with a knife while cutting Parmesan cheese at home, qualified fourth on a non-works LCR Honda.
Dovizioso leads Marquez by nine points in the standings with six rounds remaining. Vinales is third and 13 points behind the Italian while Rossi is fourth, 26 points off the lead.
Marquez fell moments before the chequered flag signalled the end of the session but his best lap was good enough for third.
"I went a little bit wide, I touched the kerb and I lost the front. My mistake," said the Spaniard, who had already eased off before sliding out at turn 13 after running wide.
Team mate Dani Pedrosa, last year's winner at Misano from eighth place, qualified seventh this time.
(Reporting by Alan Baldwin, editing by Clare Fallon)
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