The apps must now explain to the government what steps they are taking to protect children on their sites, after an investigation claimed minors are put at risk of sexual exploitation through evading the age checks put in place.
The report, which was carried out by the Sunday Times newspaper, found that more than 30 cases of child rape have been investigated by police since 2015, after victims evaded age checks to make the app believe they are over the age of 18.
A Freedom of Information request by the publication also revealed 60 further instances of child sex offences - including grooming, kidnapping and violent assault - through online dating services.
Culture secretary Jeremy Wright said: "[The investigation produced] yet more evidence that online tech firms must do more to protect children.
"[I plan to ask Tinder and Grindr] what measures they have in place to keep children safe from harm, including verifying their age.
"If I'm not satisfied with their response, I reserve the right to take further action."
New legislation coming into effect in April which requires pornography websites to use age verification technology may now also be extended to dating apps, according to Jeremy Wright.
Meanwhile, a Tinder spokeswoman said the platform used automated and manual tools and "spend millions of dollars annually" to prevent and remove underage users.
And in a statement to the Sunday Times, Grindr said: "Any account of sexual abuse or other illegal behaviour is troubling to us as well as a clear violation of our terms of service.
"Our team is constantly working to improve our digital and human screening tools to prevent and remove improper underage use of our app."