Bjoern Borg, the union's chairman, said they were calling for an international investigation into the May 31 raid and added Israel's recent easing of its Gaza blockade was insufficient.
"We don't think it is far-reaching enough," he said. "We want them to lift the blockade".
Borg said stevedores in the southwestern port of Gothenburg had already refused to handle about a dozen containers containing cargo from Israel or goods destined for it.
However, officials said they expected the boycott to have a minimal impact on Swedish-Israeli trade, which accounts for 0.2 per cent of the Nordic country's
total imports and exports.
The goods most likely to be affected will be fruit, vegetables, spices and skin care products on their way from Israel to Swedish shops.
Eleven Swedes, including crime writer Henning Mankell, took part in last month's flotilla and were briefly taken into Israeli custody.
Israel has opened its own investigation into the deaths on the aid ship but it has been criticised as lacking in transparency, although international monitors will be present.
The deadly raid sparked international condemnation and worldwide protests, and widened a rift in relations between Turkey and Israel.
Eight Turkish nationals and one US citizen of Turkish origin were killed in the raid.
History of action
Erik Helgeson, ombudsman at the Swedish Dockworkers Union, said their action was just one response to Israel's blockade on Gaza, which was tightened three years ago.
"One half of the 1.5 million people living in Gaza are children, 800,000 children, and we have to take action now," he said.
"This is our contribution, this is what we can do."
The Swedish Dockworkers Union has a history of taking action through blockades and boycotts.
Goods were stopped during both the regime of General Augusto Pinochet in Chile and apartheid in South Africa.
"The main aim is to keep the pressure on Israel so that the world focus is not turned away. It is not to paralyse their economy," Helgeson said.
But he added medical equipment and other critical goods will be let through, including equipment for dialysis machines destined for Israel from the southern Swedish port of Helsingborg.
Similar boycotts have also taken place in Norwegian and South African ports, dockworkers in Gothenburg said.