McLaren said Vandoorne, who had qualified 17th, had been ruled out by a Honda power unit problem similar to those he suffered in Friday practice.
McLaren remained last in the Formula One standings, without a point from three races and hampered by woeful reliability and a lack of performance.
Double world champion Alonso, who also had an engine failure in qualifying, started 15th and rose to 11th before retiring two laps from the end.
The Spaniard, who will miss next month's Monaco Grand Prix to race the Indianapolis 500, had already made his feelings evident in radio outbursts heard by a television audience of millions around the world.
"How they can overtake me?," he exclaimed after being passed by another rival. "(They are) 300 metres behind me, and they overtake me on the straight.
"I’ve never raced with less power in my life."
Vandoorne posted a photograph on Twitter, with a caption laced with dark humour, of himself exercising on a treadmill.
"Going for a run, you guys up to anything this Sunday?" he enquired.
Honda's motorsport head Yusuke Hasegawa had said on Saturday that the Japanese manufacturer was not sure of the exact cause of the failures.
"It is something around the bearings, it was sticking. It happened (three) times here, which is very unfortunate," he told reporters.
Alonso, asked then about the driveability of the engine, was withering in response: "I don’t care too much about the driveability if I can’t finish a race or a lap in qualifying now."
Vandoorne finished 10th on his debut in Bahrain last year as a one-off replacement for Alonso, who had been ruled out by a big accident in the opening race in Australia.
McLaren, who have not won a grand prix since 2012, were sixth overall in 2016 after ending the previous season in ninth place.
(Reporting by Alan Baldwin, editing by Pritha Sarkar and Clare Fallon)
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