In a statement, Twitter said "the upgrade must be performed to ensure the operation" of the micro-blogging tool but recognises the need to delay it and will take the risk.
"Our network partners at NTT America recognise the role Twitter is currently playing as an important communication tool in Iran.
"Our partners are taking a huge risk not just for Twitter but also the other services they support worldwide-we commend them for being flexible in what is essentially an inflexible situation."
The move was in response to further protests in Iran's capital Tehran, overnight. Tens of thousands of Iranians defied a ban and marched in protest against the outcome of last week's election result.
Much of which communicated meeting spots via Twitter.
Tweeters have thanked Twitter for its decision.
"melissaxxxxxxx Thx Twitter 4 postponing maintenance. Let freedom ring."
Since Friday's election Twitter has been the primary tool of communication for Iranians in Iran and abroad.
Instead, the planned maintenance is rescheduled to tomorrow between 2-3pm, US PST (7am EST).