The 19-year-old has flown back to the UK to attend the funeral of his aunt, bandmate Harry Styles confirmed.
"Zayn has suffered a loss in his family & has had to go home for a few days so won't be at our next shows in the US," he wrote on Twitter.
"Our thoughts are with him and his family at this sad time."
Fellow One Direction members Liam Payne, Niall Horan and Louis Tomlinson have all retweeted the message.
The 'Gotta Be You' singers have been supporting US boyband Big Time Rush on their North American jaunt.
Last week, they claimed the highest debut for a UK pop group on the US chart since the Spice Girls with their track 'What Makes You Beautiful'.
> One Direction announce UK and Ireland arena tour for 2013
Watch One Direction in the video for 'What Makes You Beautiful' below: