Ibrahim Elmi Warsame, a local member of parliament, was also killed on Wednesday as he sat at a tea shop in Puntland's capital of Garowe.
Police said they were investigating both incidents, and extra security officials were deployed in Bossaso overnight.
It was not immediately clear if the killings were linked.
Targeted killings are rarer in Puntland than in south central Somalia, where the embattled UN-backed government is fighting al-Shabab, a powerful group of fighters with suspected links to al-Qaeda.
Pirates have exploited the lawlessness to launch attacks from many towns along
Somalia's coastline, including several in Puntland.
Somalia has not had an effective central government for 18 years, although
Puntland has set up a semi-autonomous government and the northern region of
Somaliland has declared its independence.
About 19,000 civilians have been killed in fighting since the start of 2007 while another 1.5 million have been forced out of their homes.