Khaled al-Junaidi, a well-known figure in the Southern Movement, was shot in the chest when security forces opened fire while trying to arrest him on December 15, activists told AFP at the time.
"Yemeni authorities should credibly and impartially investigate the apparent extrajudicial execution of a leading political activist," New York-based HRW said in a statement.
HRW noted that authorities had announced the establishment of a committee to investigate the killing but pointed out that no arrests had been made.
"The Yemeni government has an abysmal record of holding security force members accountable for serious rights abuses," said Sarah Leah Whitson, Middle East and North Africa director at HRW.
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"Failing to seek justice in the killing of Khaled al-Junaidi will only fuel anti-government resentment and send a message that the security forces are beyond the reach of law," she said.
Junaidi, 42, was killed on a day of civil disobedience by secessionists in Aden, the capital of formerly independent South Yemen.
Junaidi was released from prison in December after serving five months for separatist activities and had been preparing to take part in the day of action.
London-based Amnesty International has called on Yemeni authorities to investigate Junaidi's killing, describing it also as an "extrajudicial execution".
South Yemen became independent after the end of British colonial rule in 1967, before it joined the north in 1990.
The Southern Movement has been staging a regular sit-in in central Aden since mid-October to demand secession.