The figure is more than ten times what it was for the 2016 election when 2,000 islanders applied.
Postal voting packs have already been sent to UK and overseas addresses, and will be delivered to local ones this week.
The government has now issued the following information to voters:
If you have registered for a postal vote, you must use your postal vote - you will not be issued with a ballot paper in a polling station.
Completed postal votes should be returned by post, however if you miss the return postal deadline your postal vote can be dropped off to any polling station on 7 October before 8pm. If this is necessary, your pack must be completed as per the instructions in the postal pack and then hand delivered to a member of the Polling Station Team. You must not put your postal vote into the ballot box.
Your postal vote pack must be returned by 8pm on 7 October. Please check postal collection times to ensure your pack arrives before the deadline.
You do not have to use all 38 votes. You can vote for as many as you want to up to a maximum of 38, but if you vote for more than 38 your entire ballot paper will be spoilt and your votes will not count.