"As has always been the case, you can receive a refund at any time," the company said in an email to one of its customers. Reuters has seen a copy of the email.
Starlink, a division of Musk's SpaceX aerospace company, has already received over 5,000 pre-orders for its devices in India but is struggling to receive commercial licences without which it cannot offer services in the country.
"Unfortunately, the timeline for receiving licences to operate is currently unknown, and there are several issues that must be resolved with the licensing framework to allow us to operate Starlink in India," the company said in the email.
"The Starlink team is looking forward to making Starlink available in India as soon as possible," it said.
Starlink is one of a growing number of companies launching small satellites as part of a low-Earth orbit network to provide low-latency broadband internet services around the world, with a particular focus on remote areas that terrestrial internet infrastructure struggles to reach.
But the Indian government has advised people against subscribing to Starlink without a licence and ordered the company to refrain from taking bookings and rendering services.
Starlink is planning to apply for a commercial licence in India by the end of January, its country head Sanjay Bhargava had said in a social media post last month, and a presentation showed that with an April roll out it targeted 200,000 devices in India by December 2022.
However, in a LinkedIn post on Tuesday Bhargava said he has stepped down as country director and board chairman due to "personal reasons". According to his profile on the platform, he had taken up the role in October.
Starlink's rivals include Amazon.com's Kuiper and OneWeb - a collapsed satellite operator rescued by the British government and India's Bharti Group.
(Reporting by Aditi Shah in New Delhi, Abhirup Roy in Mumbai and Akash Sriram in Bengaluru; editing by David Evans and Arun Koyyur)