The chart-topping singer said “everyone’s health and safety remains our top priority” as he pushed back tour dates in South America, Mexico, Australia and New Zealand.
He added: “I really hope to play the shows as planned for 2021 but will continue to monitor the situation over the coming weeks and months.
“I can’t wait to see you all on the road as soon as it’s safe to do so.”
Styles, 26, had been set to take his Love On Tour tour to Monterrey, Mexico, at the end of the month.
This would have been followed by performances in Brazil, Argentina, Chile, Peru, Colombia, New Zealand and Australia.
The North American and European dates had previously been pushed back to next year.
They included a planned Halloween-themed “Harryween” at New York’s Madison Square Garden.
Styles’s most recent album Fine Line was released in December last year and was supported by the singles Lights Up, Adore You, Falling and Watermelon Sugar.