The delay could benefit Facebook, which last week said the changes would render one of its mobile advertising tools "so ineffective on iOS 14 that it may not make sense to offer it on iOS 14."
Apple announced new privacy rules in June that were slated to take effect with the launch of its iOS 14 operating system this fall.
Among them is a new requirement that advertisers who employ an Apple-provided tracking identifier, or other tools that have a similar function, must now show a pop-up notification asking for tracking permission.
Apple said on Thursday that developers will still have the option to use the prompt when iOS 14 arrives.
"When enabled, a system prompt will give users the ability to allow or reject that tracking on an app-by-app basis," Apple said in a statement.
"We want to give developers the time they need to make the necessary changes, and as a result, the requirement to use this tracking permission will go into effect early next year."
Digital advertising firms will have space in the notification to explain why they are seeking tracking permissions, but they expect most users will decline to grant that permission.
Apple said on Thursday that it will not begin enforcing use of the prompt until early next year.
Advertisers are instead gearing up to use a new advertising system that Apple has created and claims is more private because it does not provide detailed information about individual users.
Advertisers have said that system is likely to generate less revenue.
The news was first reported by technology news website The Information.