The Navy personnel were on duty under the Maritime Task Force (MTF) deployed as part of the United Nations Peacekeeping Mission.
The condition of senior warrant officer Harun-Or-Rashid has been described as critical.
He is undergoing treatment at American University of Beirut Medical Centre, the ISPR said in a press release on Wednesday.
The other victims were taken to Hamoud Hospital after they were given first aid under the supervision of United Nations Interim Force In Lebanon (UNIFIL).
All the victims are crew members of Bangladesh Navy's ship 'Bijoy'.
The authorities concerned are now assessing the losses caused by the explosion and the Head of Mission and Force Commander and Maritime Taskfoce Commander of UNIFIL are supervising it closely.
Major general Jahangir Al Mustahidur Rahman, Bangladesh ambassador in Lebanon, visited the BN 'Bijoy' and provided all-out support to ensure treatment of the victims.
The warship of Bangladesh Navy has been participating in United Nations Peacekeeping Mission in Lebanon since 2010.
Bangladesh Navy had 110 members deployed in the UN peacekeeping mission in Beirut BANCON-8 in 2018.
Now they are serving as BANCON-10 Contingent from 8 July, 2019.
Besides, 80 Bangladesh citizens were injured in the incident.
State minister for foreign affairs M Shahriar Alam has requested the affected Bangladeshi community members to contact Bangladesh embassy for necessary support.
He said Bangladesh stands ready to support in any ways possible.
"Our thoughts and prayers for our brothers and sisters in Beirut affected by the massive explosions," he tweeted.
Meanwhile, US ambassador in Dhaka Earl Miller said that in a global community each tragic event has far reaching effects.
"My thoughts go out to everyone impacted by the explosions in Beirut, including the injured Bangladesh Navy crewmembers of the BNS Bijoy and their families," he tweeted.
Around 1, 50,000 Bangladeshis work in Lebanon in a number of sectors.
At least 100 people were killed and several thousand injured in Tuesday's massive explosion, officials said on Wednesday.
An official with the Lebanese Red Cross said at least 100 people were killed and more than 4,000 were wounded.
The official, George Kettaneh, said the toll could rise further, reports AP. \