The targeted suicide attack on Christians in a crowded Lahore park killed more than 70 people, nearly half of them children.
Facebook's Safety Check system activates after a tragedy to help people let others know they are safe.
The social network blamed a "bug" for the warnings sent to people thousands of miles away from Pakistan.
Responsibility for the attack on Sunday has been claimed by a Taliban splinter group called Jamaat-ul-Ahrar, which said it targeted Christians celebrating Easter.
On this occasion, many were made anxious when they received a message because it simply asked "Are you affected by the explosion?" without giving information about how close that person was to any potential threat.
Reports said Facebook users in the US, India, UK, Hawaii and many other places wrongly received warnings. Many shared images of the messages on social networks.
"This kind of bug is counter to our intent," it added.
"We worked quickly to resolve the issue and we apologise to anyone who mistakenly received the notification."
The problem is the latest in a series that the Safety Check feature has suffered. Last year, Facebook began to use the system more widely after being criticised about when it was employed.
Criticism was levelled at it because it was used for the large-scale attacks in Paris but not subsequently for similar bombings in Beirut.
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