In August, it will block the Flash-powered parts of webpages that were "not essential to the user experience".
The browser developer said its action would mean webpages loaded more quickly and made crashes less likely.
In 2017, it said it planned to introduce a system that would mean users must click to activate Flash no matter where it was used on a webpage.
In a blogpost, Firefox developer Benjamin Smedberg said its first step would tackle the Flash-based parts of a webpage that users did not see. This includes files used to help with tracking and following which websites users visit, to aid advertising.
Many of these hidden functions can now be done using HTML - the language of the web - said Mr Smedberg.
This list of blocked files would gradually be expanded to those Flash files used by advertisers to see if their ads were being watched, he said.
Tackling these hidden and ad-related files should cut crashes and page "hangs" by up to 10%, he added.
Statistics gathered by Mozilla showed a steep fall in the number of times webpages crashed when Google and Facebook stopped using Flash for video and replaced it with HTML-based code.
He said the change would also make the Firefox browser more secure and could mean longer battery life on some portable devices.
In 2017, users will have to click to activate Flash for any webpage content. Mr Smedberg urged sites that rely on it to show video or games to adopt HTML-based alternatives as soon as possible.
Mozilla's decision follows similar action by Google, Microsoft and Apple to phase out support for Flash.
Mozilla is planning to end full support for Adobe's Flash software in its Firefox browser from next month.