The coordinated blasts in six areas in oil and tea-rich Assam came less than a week after the separatist United Liberation Front of Asom (ULFA) rejected an offer of peace talks with the government.
Security was tightened in the commercial capital, Guwahati, and across Assam, outside government buildings, oil installations and shopping centres - all sites which ULFA, fighting for an independent state, has targeted in the past.
Nobody has yet claimed responsibility for the latest attacks, but police said they had intelligence intercepts suggesting ULFA was behind the blasts.
"They are trying to show their strength after rejecting the government's peace offer," said police inspector general DK Pathak.
The group spurned Prime Minister Manmohan Singh's offer of talks, saying it could not accept Singh's demand that they first give up violence.
India's northeast is home to hundreds of tribes and dozens of insurgent groups, some fighting for secession and others for autonomy.
Indian soldiers say grenades still
get through security checks
They blame New Delhi for plundering the region's resources of oil and timber and neglecting the local economy.
Tuesday's blasts took place exactly a year after India's tiny neighbour Bhutan launched a military offensive against ULFA to throw them out of the Himalayan kingdom where they had set up dozens of camps.
Pathak said police had intercepted messages from ULFA commanders instructing cadres to launch strikes to observe Revenge Day on 14 December, to mark the first anniversary of the operation against them in Bhutan.
Another police official said it was not easy to prevent grenade attacks, despite advance warning and heavy security checks.
"Throwing a grenade is not at all difficult for the militants because they can hide it in their body or inside handbags and then hurl it in a crowded place," said police superintendent Hiren Nath.
Calls for peace
But in the neighbouring state of Nagaland, two exiled leaders of another powerful rebel group urged followers to support a peaceful end to their revolt which has seen thousands of deaths.
"They are trying to show their strength after rejecting the government's peace offer"
police inspector general
Isak Chishi Swu, chief of the National Socialist Council of Nagaland, and General Secretary Thuingaleng Muivah, returned home to a hero's welcome on Tuesday.
The group, which has been fighting for a separate Naga nation for more than half a century, has been observing a ceasefire with Indian forces in Nagaland since 1997, but talks to end the revolt have made slow progress.