The girl band - made up of Perrie Edwards, Jake Thirlwall, Leigh-Anne Pinnock and Jesy Nelson - were due to shoot the video in Brazil but had to cancel because their team were concerned about the virus, which has now killed nearly 9,000 worldwide.
The rescheduled filming was due to get underway in the UK this week, but such plans have also been shelved.
A source said: "The girls’ well-being is of utmost priority to everyone so a video shoot for this week has been canned."
Perrie was also unwell and had to skip the group's gig in Sao Paulo.
The source added to The Sun newspaper's Bizarre column: "Perrie was unable to make a gig in Brazil at the start of the month because she was unwell and no one wants to risk anyone else getting poorly."
Little Mix had to axe plans to film the music video in South America after crew members issued concerns that they may have to be quarantined for two weeks upon their return from Brazil.
As a result, the band flew to the country to play at a festival in Sao Paulo but didn't shoot the video.
A source said last week: "They are looking into different locations and schedules to make sure they can get brilliant visuals for their new single.
"They will be filming it somewhere else once Perrie is feeling better and the other girls have returned from Brazil.
"But they know they are up against the clock to make sure it is all done in time."
