The government said one person had drowned while swimming in the northern province of Thanh Hoa and 11 people, including the six fishermen, were missing.
A child also drowned when a barge capsized in the northern province of Quang Ninh, a local newspaper said.
Vietnam Airlines said it would resume operations on Sunday and planned extra flights to help passengers from the 10 flights it cancelled on Saturday.
The Philippines was the worst hit by Conson, and on Sunday raised its death toll to 68, with 84 people still missing.
Benito Ramos, head of the civil defence office in the Philippines, said most of those killed had drowned after 40 fishing boats sank.
He said Conson caused minimal damage to infrastructure and farm production and only 2,500 people remained at temporary shelter areas after nearly 30,000 homes were either destroyed or damaged by flooding and strong winds.
Two people were killed in China.