The Styles show was to be held at Meridian at Island Gardens, a concert venue on Watson Island along the MacArthur Causeway between Miami and Miami Beach.
"The fire department would not let us do the show under any circumstances. Please stay safe," Styles tweeted around 1 a.m. ET Saturday.
Pepsi, the sponsor behind the concert, said it planned "to do what we can to make this right."
“For all attendees of tonight’s Planet Pepsi Zero Sugar Party, we understand this is disappointing," the company said in a statement, "and want to do what we can to make this right. We are offering a full refund for tonight’s show and for your ride share from the venue. Details coming soon.”
Earlier, videos posted on social media showed fans streaming out of the venue after the show was called off. Some fans were seen walking through water that appeared to be ankle-deep.
Other social media posts showed the sign posted on the concert stage: “Attention: Extreme weather is approaching. Please calmly make your way to the exits now.”
Some fans on social media complained of being forced out into the rain, while others complained of a lack of adequate restroom facilities.
Earlier, some fans posted video of the gathering crowd singing “Happy Birthday” to Styles as they waited for the concert to begin. Saturday is the former One Direction member’s 26th birthday.
On Thursday night, Styles made a surprise appearance at a Lizzo concert in the area.
The planned concert was among many scheduled in the area this week, as NFL fans flock to the city for Sunday’s matchup between the San Francisco 49ers and the Kansas City Chiefs at Hard Rock Stadium in nearby Miami Gardens, north of Miami.
Lady Gaga is scheduled to perform at the same concert venue Saturday evening. There was no immediate word about whether the Lady Gaga show will be postponed.
For Friday night, the National Weather Service had warned of severe thunderstorms in the area until 3 a.m. ET Saturday, with the possibility of tornadoes, hail and 70 mph wind gusts.
More rain is expected in Miami on Saturday – but none is expected on Super Bowl Sunday, according to The Weather Channel.