United were 2-1 down at the Emirates Stadium when referee Craig Pawson pointed to the spot after a Nuno Tavares handball.
Fernandes stepped up and sent goalkeeper Aaron Ramsdale the wrong way, but saw his effort hit the post and go wide.
It's the second penalty he's missed this campaign and many wondered why Ronaldo, who had scored earlier in the game, didn't take it.
The five-time Ballon d'Or winner has taken United's last three penalties but interim manager Rangnick confirmed Ronaldo let Fernandes take it.
He told talkSPORT: "The two of them talk about it and Cristiano told me he didn’t feel well enough, or didn’t feel as though he should take the penalty – and that’s why Bruno took it."
Ronaldo missed Tuesday's defeat to Liverpool after the tragic death of his newborn son.
The 37-year-old and partner Georgina Rodriguez confirmed the news on Monday while also confirming the birth of their daughter.
When asked if Ronaldo's decision was impacted by that, Rangnick replied: "I don’t know. You’ll have to ask him. They’ve both taken penalties and converted penalties, so it’s up to the two of them to decide."
Arsenal took the lead inside three minutes through Tavares, after David de Gea had tipped away a Bukayo Saka effort.
Saka would get on the scoresheet from the penalty spot after being fouled by Alex Telles just after the half hour mark.
Ronaldo got United back in it two minutes later and the away side did have their chances, but failed to convert.
Fernandes' miss in the second half swung the game in Mikel Arteta's side favour and Granit Xhaka's long-range effort wrapped up all three points for Arsenal.
United are now six points off fourth place with four games to go and Rangnick thinks their chances of qualifying for next season's Champions League are slim.
The German admitted: "It’s mathematically not impossible, but it’s not very realistic.
"A win today, or at least a draw after being 2-0 down, would’ve helped us."
Arsenal, meanwhile, are back up to fourth and have Champions League qualification in their own hands.
Bitter rivals Tottenham Hotspur are their closest challengers and the two teams meet in the North London derby on May 12.
Featured Image Credit: Premier League
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