Europe's new GDPR data privacy law was introduced on May 25 to combat how technology giants like Alphabet's Google and Facebook gather and handle personal information.
Continental is concerned that it could be exposed to the new law as, in the German firm's opinion, responsibility for compliance has been shifted towards app users. It said that to meet GDPR requirements, a user of the messenger platforms would have to contact everyone in their contact list.
"The risks this poses in terms of data protection are not ones the company is willing to take," it added.
Describing data as an "obligation," Continental CEO Dr. Elmar Degenhart called on tech firms to make it easier for users to comply with the new rules.
In response, Snap Inc said Continental is wrong to suggest that GDPR shifts the compliance burden on to an app user.
In an email to CNBC, the messaging service said it was "completely up to the user whether they wish to grant access to contacts in Snapchat" and any uploaded data can be deleted at any time.
Snap Inc added that it doesn't store non-user contacts.