In a letter sent to the Estonian environment minister, Fatou Diakite, the judge heading the Ivorian government investigation commission, asked Estonia to take "all measures to immobilise the ship Probo Koala".
Diakite said: "The aim is to have at our disposal the ship and its crew because we think they can give us the information we need for our inquiry."
Activists from the environmental campaign group Greenpeace are blockading the ship in the Estonian port of Paldiski and are demanding a European inquiry.
A health ministry spokesman said on Tuesday that an eighth poisoning victim, a taxi driver, had died on Sunday in the Abidjan suburb of Koumassi, not far from the port.
He said: "He was contaminated and had breathing difficulties and a distended stomach. He was being monitored at a health centre in Koumassi but he died at home.
"We do not know at this stage whether he had transported the substance."
By Monday, medical personnel had carried out some 80,000 consultations since the dumping.
France has sent experts to help clean up the waste and a French embassy official told Reuters it would be shipped to a specialist disposal plant next month.
Experts say the waste contained poisonous, foul-smelling hydrogen sulphide.
The crisis shook the world's top cocoa producer, stretching health services and forcing the government to quit as tens of thousands of people made sick by toxic fumes sought medical care for vomiting, stomach pains and other symptoms.
Trafigura, the Dutch-based oil trading firm which chartered the ship that offloaded the waste, insists it was 'chemical slops', a mixture of gasoline, spent caustic soda and water and a normal by-product from cleaning tanks used to transport fuel.
Trafigura had contracted a local company, Tommy, to remove the slops and says it warned Ivorian authorities that the waste needed to be disposed of properly.
Ivory Coast has charged and imprisoned 10 people, including two French executives of Trafigura who arrived there last week on what the company called a "humanitarian visit".
Mamadou Kone, the justice minister, refused to say when the two may appear in court.
He said: "It is a question of security because some people could arrange to help them escape."