Funerals typically take place within a few days, since remains must be cared for and buried quickly. Since there is no casket present, memorial services offer a little more leeway for the family.
A memorial service is intended to allow closure for those still living and function as an important part of the grief process. Additionally, it acts as a show of support to those closest to the deceased. For these reasons, it should be held shortly after the death. Typically, the service is scheduled to occur within a week, or two at most. It is best not to wait much longer than that. Death didn't wait for a good time, neither does grief. The memorial service is a response to both of those things, so do not worry about choosing an inconvenient time. Do it quickly.
If a few weeks have passed and no memorial service has been held, I recommend considering whether it is going to help bring closure and support, or if it will drag out the grief of the loved ones. There is an emotional strain associated with an "official" service, and if more than three or four weeks have gone by, the appropriate time for this has usually passed.
If the intention is simply to honor and celebrate the memory of the loved one's life, consider having a less formal gathering, perhaps in someone's home. Have each person bring a photo of the deceased or a card that loved one wrote. At that time, share stories and memories, compile the items in an album, and present it to the next of kin as a gift.