The Facebook-owned app saw its ranking drop in both the UK and the US after users received messages asking them to consent for Facebook to access their data, including their phone numbers and information about how they interact with others.
The update will come into force in just 27 days on February 8, and users in affected regions will have to have consented by that date, even if they do not have a Facebook account.
That's according to App Annie, a global provider of mobile data and analytics, cited by MailOnline as revealing the app has dropped to number 38 in the US downloads chart and 10th place in the UK, much lower than usual.
The update affects users where there are tough data protection laws.
Users received notifications asking them to consent or lose access to their accounts.
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WhatsApp, which was acquired by Facebook in 2014, says the data sharing is to help Facebook "improve its products or advertisements".
Signal and Telegram messaging apps are seeing a sudden increase in demand after larger rival WhatsApp's updated terms of service raised eyebrows on social media.
WhatsApp, which uses Signal's encryption technology, laid out fresh terms on Wednesday, January 7, asking users to agree to let owner Facebook Inc and its subsidiaries collect user data, including their phone number and location.
Some privacy activists questioned the "accept our data grab or get out" move on Twitter, and suggested users to switch to apps like Signal and Telegram.
Signal's popularity shot up further on Thursday after it was endorsed by Elon Musk, who has one of the most-followed accounts on Twitter, and by the micro-blogging site's top boss Jack Dorsey.
More than 100,000 users installed Signal across the app stores of Apple and Google in the last two days, while Telegram picked up nearly 2.2 million downloads, according to data analytics firm Sensor Tower.
New installs of WhatsApp fell 11 per cent in the first seven days of 2021 compared with the prior week, but that still amounted to an estimated 10.5 million downloads globally, Sensor Tower said.
Writing on Twitter, one former WhatsApp user said they had just deleted WhatsApp and Instagram - also owned by Facebook Inc. from their phone - as "their new terms and conditions freak me out".
Another commented: "I deleted my WhatsApp last week. I definitely lost some contacts, and that sucks, but I've come to see FB as a criminal enterprise; I can't afford to give them access to my data."
While another wrote: "Deleted my WhatsApp today. I've been using Signal for a while and think it's brilliant. hope y'all will join me over there!"
"We may use the information we receive from them, and they may use the information we share with them, to help operate, provide, improve, understand, customise, support, and market our Services and their offerings, including the Facebook Company Products."
Facebook Inc. will be able to access your account information such as your phone number, your IP address, which browser you use, your time zone and language used, data on your interactions with other users and time logs showing how long you use the app for and how frequently.
WhatsApp is an encrypted app so Facebook will not be able to see the actual contents of messages you send.
The app, which boasts two billion active users, is sending users a pop-up asking them to agree to share data with Facebook.
Many users have seen the pop-up message and clicked the 'agree' button without reading the terms in the small print.
A spokesperson added: "For the avoidance of any doubt, it is still the case that WhatsApp does not share European region WhatsApp user data with Facebook for the purpose of Facebook using this data to improve its products or advertisements."
"There are no changes to WhatsApp's data-sharing practices in the Europe arising from this update. It remains the case that WhatsApp does not share European Region WhatsApp user data with Facebook for the purpose of Facebook using this data to improve its products or ads.
"It's also about improving how businesses use WhatsApp to connect with customers. The updated Policy provides info on how businesses using the WhatsApp API to talk to customers can now do so using a Facebook-provided service to help them manage their chats with customers."
WhatsApp is part of Facebook founder Mark Zuckerberg's social media empire, which also includes Instagram, and these changes are being made to help it integrate better with other services offered by the dominant force.
It is believed Zuckerberg is looking to take steps towards eventually integrating his three massive social media platforms into one.
Will Cathcart, head of WhatsApp, said in a tweet: "It's important for us to be clear this update describes business communication and does not change WhatsApp’s data sharing practices with Facebook.
"It does not impact how people communicate privately with friends or family wherever they are in the world."