The bureau initially retweeted the prime minister's photo of himself looking through a plane window, with submerged fields and buildings visible.
Hours later, they tweeted the same image again, but with a much clearer scene crudely pasted on to the window.
The second tweet was deleted but not in time to prevent social media ridicule.
The PIB has made no public comment yet.
Mr Modi flew to Chennai (Madras) in Tamil Nadu state on Thursday to see the damage caused by the widespread flooding, which has left more than 260 people dead since last month.
A large-scale rescue operation is under way, amid neck-high water in some areas.
While some saw the deleted tweet as light relief, others criticised it as inappropriate amid the tragedy. Others also shared their own edited Modi pictures.
It isn't the first time Mr Modi has fallen victim to some amateur image editing.
Last year, before Mr Modi became prime minister, a fake photo showing US President Barack Obama watching one of his speeches went viral.
Commentators on Twitter suggested the image was released by an ardent Modi supporter trying to imply the US president was following Mr Modi's election campaign.
India's state-run Press Information Bureau is facing online mockery after tweeting an edited image of PM Narendra Modi surveying deadly Chennai floods.