According to audience tracker AppData.com, over the past week the number of daily Instagram users fell by 3.5 million to an average of 12.4 million users per day.
Instagram has disputed the data.
Facebook shares sank about 2.5 per cent lower in early trade, before rebounding to $25.71 in the early afternoon, off 1.2 per cent.
Earlier this month, Instagram backed off planned policy changes that appeared to clear the way for the mobile photo sharing service to sell pictures without compensation, amid protests from users.
Changes to the privacy policy and terms of service had included wording that appeared to allow people's pictures to be used by advertisers at Instagram or Facebook worldwide, royalty-free.
Twitter and Instagram forums buzzed over the phrasing, as users debated whether to delete their accounts before the new rules kicked in.
Facebook acquired Instagram earlier this year. The original price was pegged at $1 billion but the final value was less because of a decline in the social network's share price.
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It doesn't pay for sites to try and out-smart their users, but these guys never learn.