Company executive Eddy Cue revealed the figure during an interview with USA Today, in which he also confirmed that 2 million of those customers have signed up for a family membership.
"We're thrilled with the numbers so far," he told the publication.
Apple Music offers users access to 30 million tracks during the three-month trial, with the monthly subscription priced at $9.99/£9.99 for an individual account, or $14.99/£14.99 for a family account.
The service will be weighed and measured in just under two months when it transpires how many of those 11 million subscribers will take out premium accounts.
By comparison, market leader Spotify confirmed in June that it has 20 million premium subscribers and 75 million active users.
Cue also revealed that July was a record month for the App Store, with strong growth in China helping it reach $1.7 billion in transactions.