The Spaniard's Belgian rookie team mate Stoffel Vandoorne was absent from the grid in Bahrain two weeks ago due to a problem with the Honda power unit.
Alonso, who is due to race the Indianapolis 500 next month instead of the showcase Monaco Grand Prix, had qualified in 15th place in Sochi.
However, the car broke down on the formation lap at the pit lane entry, forcing the start to be aborted with the cars going around again as the unhappy Spaniard unbuckled himself and stepped out.
Honda said Alonso's car had suffered a loss of power due to a suspected energy recovery issue in the hybrid unit.
"It's obviously frustrating. Four races into the championship, four DNFs (non-finishes). This time we did not even make the start. That's sad but there's nothing we can do," Alonso told the BBC.
"I come here, drive as fast as I can to try and help the team. We just hope the next race will be better. I'm just a driver. I help the team but the team have to look at the bigger picture."
McLaren, the second most successful team in the sport's history in terms of wins, have not won a race since 2012 and are experiencing new lows every weekend with the engine lacking power and reliability.
They have yet to score a point in three races this season and Vandoorne started at the back of the grid in Russia due to a 15-place penalty incurred as a result of excessive engine component usage.
Honda, who have borne the brunt of the criticism, announced on Sunday a deal to supply Sauber with engines next season in addition to McLaren.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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