The purported hostage said he was 33 and kidnapped more than a year ago in Sanaa in the video dated December 2014.
In the video, the hostage said he was looking for help and that his life was in danger.
The photojournalist was kidnapped in the Yemeni capital in September 2013, the US-based monitoring agency said citing reports.
The video features a message by Nasser bin Ali Al-Ansi, of Al-Qaeda in the Arabian Peninsula, threatening to kill him three days "after the issuance of this statement" if Washington failed to meet the group's demands.
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AQAP is considered by Washington as the most dangerous affiliate of Al-Qaeda.
Yemen is a key US ally in the fight against Al-Qaeda, allowing Washington to conduct a longstanding drone war against the group on its territory.
The militant group has exploited instability in the impoverished country since a 2011 uprising overthrew president Ali Abdullah Saleh.