Abdullah was scheduled to address the rally in Magam town of central Badgam district, 30 km from Srinagar.
"Fourteen people were injured in the explosion. Of them, 10 have been taken to hospital," a police official said, adding that they were investigating the explosion.
Eyewitnesses said some unidentified persons threw a hand grenade causing the explosion.
Earlier, another explosion occurred 50 metres from an election rally being addressed by Abdullah in Khanyar area of the state capital.
Abdullah, who was accompanied by other NC leaders, told the rally: "These explosions will not deter me and should also not deter you from coming out and voting for the National Conference."
"You must come out in large numbers and vote for the NC on April 30," he said.
Police said no one was hurt in the Khanyar blast.
No one has so far claimed responsibility for the explosions.
If India becomes communal,Kashmir not to remain with it: Farooq Abdullah
Union Minister and National Conference president Farooq Abdullah today said communalism is not acceptable to the people of Kashmir and they will not remain with India if the country becomes communal.
"Pray to God to save us from communal forces so that we can move forward. India cannot become communal. If it becomes communal, then Kashmir will not remain with India. Communalism is not acceptable to Kashmiris," Abdullah told a poll rally at Khanyar in old city.
The NC head took a dig at BJP leader Griraj Singh and VHP's Praveen Togadia, saying "they say those who do not vote for Modi should go to Pakistan. (I say) Those who vote for Modi should drown in the sea."
The nation belongs to its people and they will decide what to do, he said.