Mohammed al-Qadhi, a correspondent working in Sanaa for the Emirati The National newspaper, told Al Jazeera that witnesses had later seen the man surrendering after a gun battle with police.
"There was exchanges of fire between him and the police of the hospital which continued, according to eye witnesses, for almost half an hour," he said.
"Police managed to storm the room where he was by firing tear gas, and the room was seen to be burning.
"Witnesses told me they saw the gunman raising his hands and surrendering but whether he was killed or injured they don't know. The authorities are not telling us."
An unnamed hospital source told the Reuters news agency that the man took a gun from one of two guards in his room where he was being treated and opened fire, wounding both, before trying to make his way downstairs, where more fighters opened fire at the entrance before escaping.
Al Arabiya television reported that the two guards were killed.
Yemen has become a major security concern for Western nations and Arab neighbours Saudi Arabia, who fear al-Qaeda are using the country's instability to recruit and train fighters.
As well as tackling secessionist sentiment in the South and fighting al-Qaeda, the government is also trying to bring an end to a Shia rebellion in the North.