The Americans, aged 43 and 44, were working aboard the Maersk Alabama as security contractors.
Their bodies were discovered in a cabin on the ship while it was docked in Port Victoria in the Seychelles on Tuesday.
Tom Hanks as Captain Phillips, based on the Maersk Alabama hijacking
Maersk Line Ltd spokesman Kevin Speers said on Friday a police report revealed drugs and paraphernalia were found in the cabin. However, the type of drug is unknown.
"We are saddened by the tragedy and our thoughts are with the family and friends of the deceased men," said Mr Speers.
He added the ship had left the African port after being given the green light by officials to leave the Seychelles following an on board investigation.
Capt Richard Phillips was held hostage in 2009
Police spokesman Jean Toussaint said post-mortems would be carried out, adding there was "no evidence of physical trauma" on either man's body.
The ex-Navy Seals were part of a ship crew of 24 members who arrived in Port Victoria on February 16, and were expecting to leave two days later.
They worked for a Virginia-based maritime security firm, The Trident Group
In a statement posted on its website, the firm's president Thomas Rothrauff said there were was "no immediate indication as to the cause of death, but the deaths were not caused by operational activity."
The Maersk Alabama was made famous during its 2009 hijacking off the coast of Somalia.
The ordeal ended when Navy Seals snipers shot and killed three pirates holding Captain Richard Phillips hostage aboard a lifeboat.
The story inspired the 2013 film Captain Phillips, starring Tom Hanks.