1. You can have one as soon after giving birth as you are comfortable
Short Answer: Every new mom has a different birth experience, and every new mom feels differently after giving birth. If there are no major complications, the new mom can have a postnatal massage as soon as she feels comfortable being touched.
More details: In some cultures, massage for new moms begins as soon as the baby is out and happens every day to help with their recovery from the trauma of the birthing process. Personally, after my first daughter was born I didn't want anything or anyone to touch me, and the thought of human touch other than my baby physically made my stomach turn. So ultimately, there is no set "time" that a mom has to wait to receive a postnatal massage. It is completely up to her, how she feels physically and mentally, if she feels she has the time and desire to get away for an appointment, and the advice of her doctor if there were any complications. If there were any complications such as a C-section, her therapist can make needed adjustments with propping and cushioning to make sure she is comfortable. The ultimate goal is her comfort and healing, so timing is up to her.
2. It may help your uterus shrink faster
Short answer: The big "pregnancy belly" doesn't completely go away once baby is out. It can take some time for the uterus to recover and return to it's original size. Massage can help increase circulation, and improve the condition of the muscles and organs so things get back to "normal" sooner.
More details: Whenever anyone comes for a massage with a condition that has been there a while, I tell them that "it didn't get this way overnight, it isn't going to get fixed overnight". Pregnancy belly is the same. It took 40ish weeks for the uterus to grow and stretch, and dislocate a good portion of the skeleton in the process, just because the baby is removed, doesn't mean everything "snaps back" instantly. It can take time for everything to recover and return to normal, and massage can help increase the circulation and tone the muscles and organs so that things get back in the right sizes and places more quickly and easily.
3. It may help fight "baby blues"
Short answer: It is completely normal for new moms to not feel completely happy all the time after giving birth. Extreme changes in hormones, new mom stress, and lack of sleep can cause some sadness. Massage can help calm hormones and release the "good" ones that can help improve mood and happiness.
More details: It is ok to not feel ok after giving birth. Many new moms have difficulty not feeling totally euphoric after giving birth, and it is easy for them to get even more upset that they feel that way. Society doesn't help much, almost criticizing new moms for not feeling happy about their new baby all the time, which further contributes to stress and upset feelings. But after a traumatic birth (and even if the birth is easy and routine, it is still a trauma on the body), everything changes in so many ways, so fast, there is a lot that new moms are facing and feeling a little blue isn't uncommon, and is actually a little normal. The major concern comes when the everyday "baby blues" becomes more serious and becomes postpartum depression, then massage may help calm some symptoms, but at that point, a doctor should be consulted.
4. Gives a new mom quiet time just for herself to relax and recover
Short answer: New moms have a lot going on, both with the daily stresses of having a new baby, everyday life which is still going on as usual, plus the physical recovery she needs to go through. If nothing else, a massage can give her a break and some care for herself which will greatly help with her recovery.
More details: Even though a new baby makes the world feel like a totally different place, the world doesn't stop moving with the new arrival. New moms are caught up in a whirlwind of trying to recover from giving birth, care for the new baby, adjust to a new routine in daily life, and that isn't if she has other children or family members that are relying on her, a job that wants her to get back to work asap, and all the other issues of daily life. New moms need time to themselves to relax and recover, so sometimes getting away for a massage is the only way that can happen. In addition to all the physical benefits of a postnatal massage, sometimes just the chance to lay quietly and grab a quick nap can outweigh all other benefits.