Walt Disney said that Disney+ has attracted more than 50 million paid users, with 8 million of them coming from India where the video streaming service was rolled out last week.
Rival Netflix, which has services available in over 190 countries, has nearly 167 million paid subscribers globally as of its last reported quarter.
The coronavirus pandemic, and the resulting move across the world towards working from home, has driven a boom in usage of online gaming, streaming and communications.
Disney+ was rolled out in eight European countries, including Ireland, the UK, France, Germany, Italy, Spain, Austria and Switzerland, in the last two weeks, the company said.
It was launched in the US in November.
The service is available in India in conjunction with the Hotstar streaming platform, which was acquired as part of Disney's $71 billion purchase of Twenty-First Century Fox in 2019.