The issue was highlighted on Reddit, where a customer showed their OnePlus 5 phone restarting when a 911 emergency call was placed.
Others said calls to 999 in the UK and 112 in Europe were also affected by the glitch.
OnePlus said it would distribute a software update to resolve the problem.
The Chinese phonemaker promotes itself as a company that sells high-end smartphones at low prices.  Its latest device, the OnePlus 5, was released in June.
On Tuesday, Reddit user Seattle_Horn posted: "I had to dial 911 on my OnePlus 5 yesterday (saw a building on fire a few blocks away) and both times I tried my phone rebooted on me."
Several contributors added that they had experienced the same problem before or had been able to replicate it.
Some said they would return their phones to the company because the glitch could "cost lives".
OnePlus said in a statement "We have been in touch with the customer and have tested a software update that has resolved the issue.
"We will be rolling out the software update shortly."
Phonemaker OnePlus has admitted a glitch in some of its devices prevented people making calls to the emergency services.