Mark Zuckerberg's firm is planning to buy the company for around £11bn.
Opponents want US regulators to stop the deal until Facebook provides more information on what it plans to do with the personal data of WhatsApp's users.
But Facebook said it will operate as a separate company and honour existing privacy arrangements, which include not collecting user data for advertising.
"WhatsApp built a user-base based on its commitment not to collect user data for advertising revenue," read a complaint filed with the US Federal Trade Commission (FTC). It was drawn up by two non-profit groups, the Electronic Privacy Information Center and the Center for Digital Democracy.
They added: "Users provided detailed personal information to the company including private text to close friends. Facebook routinely makes use of user information for advertising purposes and has made clear that it intends to incorporate the data of WhatsApp users into the user profiling business model.
"The proposed acquisition will therefore violate WhatsApp users' understanding of their exposure to online advertising and constitutes an unfair and deceptive trade practice, subject to investigation by the Federal Trade Commission."
And the groups, which work on research and consumer protection online, asked the regulators to investigate the deal "specifically with regard to the ability of Facebook to access WhatsApp's store of user mobile phone numbers and metadata".'Insulate'
Facebook, the world's top social network with 1.2 billion users, generates the majority of its revenue by showing ads that target users by age, gender and other traits.
"As we have said repeatedly, WhatsApp will operate as a separate company and will honour its commitments to privacy and security," Facebook said in a statement seen by Reuters.
Facebook announced its intention to buy WhatsApp, which has 450 million users who are able to send instant messages and other media over mobile, with cash and stock.
There is no charge for individual messages, which are sent using wi-fi or data connections, making it cheaper than SMS messaging in many cases. Other users pay around £0.60 per year subscription.
Referring to the business model, Jan Koum wrote on the WhatsApp website: "When people ask us why we charge for WhatsApp, we say, 'Have you considered the alternative?'"
Despite assurances by WhatsApp and Facebook that the privacy policies will not change, the groups noted that Mark Zuckerberg's social networking company has in the past amended an acquired-company's privacy policies.
Notably, it did so with the Instagram photo-sharing service that it bought in 2012.
Regulators must require that Facebook "insulate" WhatsApp user information from access by Facebook's data collection practices, read the complaint, which was dated 6 March 2014.
"WhatsApp users could not reasonably have anticipated that by selecting a pro-privacy messaging service, they would subject their data to Facebook's data collection practices," read the filing.
The FTC will decide whether the acquisition can go ahead and, if so, whether or not conditions should be imposed.