The other four deaths at Guantanamo, which currently holds about 290 prisoners, were the result of apparent suicides, according to the US military.
Haupt said Razzak was detained in Afghanistan in January 2003 and was a "committed jihadist", then aged 64.
He did not elaborate except to say that Razzak, who would have turned 69 next month, was accused of "actively engaging the US and its allies in Afghanistan."
"We make every attempt to preserve life here at Guantanamo and we regret any loss of life," Haupt said.
The US has drawn intense international criticism for holding foreign captives for years without charge at its naval base in southeast Cuba.
Sami al-Hajj, the Al Jazeera cameraman being held at Guantanamo, has been on hunger strike since January 7, 2007, and is believed to be in deteriorating health.
Sami was arrested in Pakistan in December 2001 whilst travelling with a legitimate visa to work in Afghanistan as a cameraman for Al Jazeera.
Since then he has been held as an "enemy combatant".
Ould Sidi Mohammed, a Mauritanian inmate recently released from the jail, said al-Hajj has an infection and has not been getting adequate medical treatment.
Mohammed said: "The last time I talked to him [Sami al-Hajj] was on the same day when I left, on September 25.
"His health condition is extremely deteriorating. He is losing weight continuously. He suffers from kidney infection and he urinates blood."
"Unfortunately, prisoners do not receive full medical treatment. Prisoners on hunger strike are isolated in special places designated to torture them to hold them back from their objectives."
Sami has never been charged.
Hopes that he would be released at the end of August on condition that he remain in his country of origin, Sudan, have proved unfounded.