Former England international Woolmer, 58, was found dead in his Jamaica hotel room the day after Pakistan lost a World Cup game to Ireland, knocking them out of the tournament.
The PCB said in a statement that the advertisement had been forwarded to the International Cricket Council, full member countries' cricket boards and other international cricket websites.
The ad, available on the board's website www.pcb.com.pk says the appointment will be for an initial period of two years starting from June 2007 and that terms and conditions are negotiable.
It asks for someone who has played at least first class cricket and who possesses "exceptional communication and man-management skills" and computer knowledge.
It also stresses good interpersonal skills "to develop and sustain cohesive team structures" -- a nod to Woolmer's success in harmonising the often fractious Pakistani team.
The new coach's responsibilities will include working closely with the selectors and the director of game development, who was named on Monday as Mudassar Nazar.
Applicants have to send their CVs to the PCB by May 15, it says.
Local media have said that former India coach John Wright, a New Zealander, and Leicestershire's Tim Boon are the favourites for the job but the PCB has stayed tight-lipped about candidates.
The Pakistan job is widely regarded as one of the toughest in World Cricket, due to the high expectations of 160 million cricket-obsessed people, language difficulties and a series of recent controversies.
Any coach will also have to virtually rebuild the team from scratch after the 1992 World Cup champions' humiliating exit from the 2007 edition in the Caribbean.
In a bid to usher in a new era, Pakistan last week appointed the relatively young Shoaib Malik as captain to replace Inzamam-ul-Haq.