Officials told CNN they expected the death toll to increase. Exit points from the northeastern state were closed and paramilitary forces were dispatched to secure oil refineries.
"There may be more blasts, you never know. But we are taking all precautions," Deputy Inspector General of Police N.I. Hussain told CNN-IBN.
No one has claimed responsibility for the attacks. Assam's home commissioner Rajiv Kumar Bora told CNN "all aspects" were being investigated regarding potential suspects.
Police reported the coordinated explosions were set off in the Assam capital city of Guwahati, and in the districts of Kokrajhar, Barpeta and Bongaigaon.
Suspicion fell on the separatist group United Liberation Front of Assam, which has waged a 20-year insurgency demanding more autonomy from the central government, CNN-IBN said. Intelligence sources said few other groups could launch such a coordinated attack.
The blasts in Assam were the latest bombing attacks in India, The Times of London reported. During the past four months, seven attacks killed about 150 people.