The Department of Non-Resident Keralites Affairs (NORKA) has also been directed to take necessary steps, the official added.
The woman's father, in the video, says the absence of his daughter's name from the letter caused anguish and affected him both mentally and emotionally.
"All news flashes were also saying three Malayalees," he said.
The father said that he has not received any updates from the state or the Central governments regarding his daughter's current status.
"It is the company, which owns the ship, that has informed me that my daughter is safe," he said.
He further said that he last spoke to his daughter on Friday.
"She calls every morning regularly. When that did not happen on the next day, we tried to call her, but could not reach her. Then in the afternoon, the company which owns the ship called and told us what happened," he said.
Meanwhile, Iran has said that Tehran will "soon" allow Indian authorities to meet the 17 Indian crew members onboard the cargo vessel.
Vijayan had on Sunday sought the intervention of the External Affairs Ministry for the safe return of the Indian nationals including three from the state who are onboard the vessel.
The ship -- MSC Aries -- was seized by Iran's Revolutionary Guards near the Strait of Hormuz on Saturday, April 13.
As per initial reports, three among the crew-Sumesh, P V Dhanesh and Syamnath were confirmed to be from Kerala.
The MSC (Mediterranean Shipping Company) said it is working closely with relevant authorities for the well-being of 25 crew members and the return of the vessel.