The decision has been made as a tribute to the huge Greek community based in the city.
Celtic Manager Neil Lennon said: "We have enjoyed our visit to Australia immensely and we very much look forward to visiting Melbourne. We are very aware of the huge Greek community in Melbourne and we thought it would be fitting tribute for Giorgios to captain the team on this occasion.
"One of the aims of our visit was to make new friends in Australia. We have done this already in Sydney and Perth having received a fantastic welcome in both cities. We are sure that we will receive the same reception in Melbourne and we thank all the fans in Australia sincerely for their continuing support."
Giorgios Samaras said: "Being named captain for the game against Melbourne Victory is a real honour and myself.and all my team mates are looking forward to this great occasion. I have a very strong family connection with Australia and it is an absolute privilege to visit such a great country again. It is even more of a privilege to do so with Celtic, such a great football club.
"Celtic is a Club which has a spirit and ethos like no other. Already we have seen thousands of supporters in Australia and we are looking forward to playing in front of thousands more fans in Melbourne next week."
Tickets are selling fast for the match, but some are still available by going to www.ticketek.com.au.