Villa was loaned to the club from Major League Soccer (MLS) club New York City, who are also owned by English champions Manchester City, and it had been hoped he would play the full 10 matches allowed to a guest player under league rules.
The club confirmed on Wednesday, however, that Villa would leave Australia in early November to fulfil marketing and commercial obligations in New York.
The club is hoping Villa could return to play more matches for Melbourne after he has settled his family in the United States.
"We would obviously want a player of his calibre to represent the club in as many games of the guest allowance as possible between now and the commencement of MLS pre-season training in January," a club spokesman said.
"The precise number of A-League games that David will play will be determined by the best interests of the player and his now New York-based family and the prioritisation of the requirements of both New York City FC and Melbourne City FC.
"That means that his playing and training schedule will be the product of all of those factors and subject to ongoing assessment."
The former Barcelona and Valencia forward has scored equalisers to rescue 1-1 draws for City in the first two games of their A-League season against Sydney FC and Newcastle Jets.
His last two matches will be this weekend's local derby against Melbourne Victory and the following week's fixture at home to Adelaide United.
(Reporting by Nick Mulvenney in Sydney, editing by Sudipto Ganguly)
