Telegram is riding high, adding tens of million of users this year. Now the bill is coming due.

The messaging service and social-media platform owes creditors roughly $700 million by the end of April, according to people briefed on the company’s plans and loan documents viewed by The Wall Street Journal. At the same time, Telegram Group Inc. must cover rising equipment and bandwidth expenses because of its rapid growth, despite going years without attempting to generate revenue.

Telegram is one of the few significant social-media challengers to Facebook Inc., on a trajectory toward one billion users active each month by the end of 2022, up from roughly 550 million today.

But first Pavel Durov, the Dubai-based Russian émigré who owns Telegram, needs to figure out how to convert his app’s momentum into a self-sustaining business.

“A project of our size needs at least a few hundred million dollars per year to keep going,” Mr. Durov wrote in his public channel on Telegram late last year. “While doing that, we will remain independent and stay true to our values, redefining how a tech company should operate.”