No presidential candidate is believed to have ever raised so much money so fast. The campaign has stopped trumpeting its fund-raising totals to keep Democrats from becoming complacent.

Vice President Kamala Harris has raised more than $1 billion in less than three months as a presidential candidate, according to three people with knowledge of her fund-raising haul, a remarkable sum of money that has remade the race against former President Donald J. Trump.

The $1 billion haul, which encompasses money raised for her campaign and affiliated party committees, including the Democratic National Committee, is being spent on a wave of...