A Buckingham Palace statement read: “Prince Philip and I join all Canadians in expressing our sadness following the terrible tragedy that occurred in Toronto yesterday.”
Her Majesty, who is also Queen of Canada, issued the statement after police confirmed that the 10 dead and 14 wounded were "predominantly" women.
They said the youngest were in their twenties and the eldest in their eighties.
The driver of the van, Alek Minassian, 25, was charged on Tuesday with 10 counts of murder and 13 counts of attempted murder.
Police say he appeared to intentionally strike pedestrians after mounting a busy pavement in a rental van.
He was arrested several blocks away after a tense standoff with police.
He showed little overt emotion as he made a brief appearance in a Toronto courtroom on Wednesday in a white jumpsuit and handcuffs. The judge ordered him detained without bond and scheduled the next hearing for May 10.
"It was like he was playing a video game, trying to kill as many people as possible," said Panna Patel, 42, who stopped by the memorial and had been at the scene a day earlier, getting cash from an ATM as it occurred.
"He was looking people directly in the eye, making eye contact, it was so scary. He wasn't remorseful at all."
Prime Minister Justin Trudeau dismissed the possibility of terrorism, saying that authorities see no national security element in the case.
He told a news conference that the incident "hasn't changed the overall threat level in Canada", though it occurred as Cabinet ministers from the G7 nations were meeting in Toronto.
Authorities so far had not disclosed a possible motive or cause, though "the incident definitely looked deliberate," Police Chief Mark Saunders told reporters at a late-night news conference.
Saunders said Minassian, who lives in the Toronto suburb of Richmond Hill, had not been known to police previously. An online social media profile described him as a college student.
The driver was heading south on busy Yonge Street around 1.30pm and the streets were crowded with people enjoying an unseasonably warm day when the van jumped onto the pavement.