The broadcasting watchdog said it had received 2,025 complaints since Friday’s programme and was deciding whether to investigate.
The 71-year-old presenter was signing off the bulletin, which was broadcast live, when he made the comments.
Referring to pro-Brexit protesters who brought Westminster to a standstill, he said: “It’s been the most extraordinary day. A day which has seen... I have never seen so many white people in one place, it’s an extraordinary story.
“There are people everywhere, there are crowds everywhere.”
The remark drew online criticism from some commentators, including broadcaster Julia Hartley-Brewer, who suggested Snow was implying being white was “a bad thing”.
An Ofcom spokeswoman said: “We are assessing these complaints against our broadcasting rules, but are yet to decide whether or not to investigate.”
Channel 4 News said it regretted any offence caused.
“This was an unscripted observation at the very end of a long week of fast-moving Brexit developments,” a spokeswoman said.
“Jon has covered major events such as this over a long career and this was a spontaneous comment reflecting his observation that, in a London demonstration of that size, ethnic minorities seemed to be significantly under-represented.
“We regret any offence caused by his comment.”
Journalists from Channel 4 News and CNN were also harassed by some demonstrators while covering rallies held by several pro-Brexit groups on Friday, the day the UK was originally scheduled to leave the EU.
Two opposition MPs leaving the Commons were subjected to public abuse by Brexiteers, who called them “traitors”.
Police made five arrests, including two for assault.
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