The City defender came close to giving the Swiss the lead just before half-time with a header that went narrowly wide.
The only goal of a tightly-contested game was scored by Switzerland’s Breel Embolo just after the interval.
Cameroon started brightly and had a great chance to open the scoring inside 10 minutes, as Bryan Mbeumo’s shot was initially saved by Yann Sommer before Karl Toko Ekambi fired over the crossbar.
Switzerland had Sommer to thank again moments later with Martin Hongla the next to try his luck, but the Swiss No.1 was there to make the save before Silvan Widmer cleared from danger.
Akanji had a great chance just before the break, but could not direct his header on target following Ruben Vargas’ corner.
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Switzerland took the lead three minutes after the restart.
A sweeping move from left to right found Xherdan Shaqiri on the wing, he drilled a low ball into the area which found Embolo in space, with the AS Monaco man firing home from close range.
Cameroon pushed to find a leveller but found Sommer in sensational form once again, this time denying Eric Maxim Choupo-Moting at his near post.
Vargas had the chance to double the Swiss’ lead on 66 minutes, a ball from the right by Shaqiri found the 24-year-old in space just outside the six yard box, but he could not find a way past Onana.
Arsenal’s Granit Xhaka had the final chance of the game as he tried from distance, but his effort was well saved by Onana.
After their win, Switzerland sit top of Group G with Ederson‘s Brazil set to face Serbia later in the day in their opening group game of the tournament. (19:00 UK)
