A delegation of senior USA officials went in the president's place to the Aisne-Marne American Cemetery and Memorial, the White House said.
Trump's remarks followed those of French President Emmanuel Macron, who used a ceremony in central Paris earlier in the day commemorating the 1918 Armistice to attack growing nationalist movements, calling them the "betrayal of patriotism".
Trump had been scheduled to lay a wreath and observe a moment of silence Saturday at the Aisne-Marne American Cemetery and Memorial, located adjacent to Belleau Wood and about 60 miles (100 kilometers) northeast of Paris.
President Trump did not visit a World War I cemetery in northern France this weekend because his motorcade would have disrupted traffic in Paris and nearby suburbs for hours, an administration official told Fox News Sunday.
The decision prompted a rash of criticism on Twitter, with Sir Nicholas Soames, a British MP who is a grandson of former prime minister Winston Churchill, saying Mr Trump was dishonouring United States servicemen.
Sir Nicholas Soames, a serving MP, wrote on Twitter: "They died with their face to the foe and that pathetic inadequate Donald Trump couldn't even defy the weather to pay his respects to the fallen".
Despite the rain, roughly 1,500 people attended a rally against Trump at a Paris plaza several miles away, according to police.
Last year, foggy weather caused similar security concerns which prevented Mr Trump from visiting the demilitarised zone between North and South Korea.
Ben Rhodes, who served as deputy national security adviser for strategic communications under President Barack Obama, said the excuse about the inclement weather did not stand up.
Obama wasn't the only one featured in the rain in Twitter messages attacking the president.
Meantime, world leaders walked together in a show of unity to the Arc de Triomphe, the site of the solemn ceremony.
Trump sat mostly stone-faced with German Chancellor Angela Merkel, Canadian Prime Minister Justin Trudeau and others as Macron spoke.
It was not clear what Trump chose to do instead of attending the cemetery. During that time he sent a tweet wishing a "Happy 243rd Birthday" to the U.S. Marine Corps.