According to reports, 17 of those are in a critical condition, and the injuries include several amputations.
President Barack Obama said those behind the attack would feel "the full weight of justice".
"We still do not know who did this or why. And people shouldn't jump to conclusions before we have all the facts. But make no mistake -- we will get to the bottom of this. And we will find out who did this; we'll find out why they did this. Any responsible individuals, any responsible groups will feel the full weight of justice," he said in a televised address.
The first explosion came at about 15:00 local time (19:00 GMT) on the north side of Boylston Street.
Seconds later, there was a second explosion further away from the finishing line.
Shortly after that, a fire broke out at Boston's John F Kennedy Library a few miles away from the explosions. It is unclear whether the incidents are related.
The FBI has taken over what it calls a "potential terrorist inquiry".
No group or individual had so far said they carried out the attack.
Image: © Getty
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