Warning: Very long philosophical diatribe below.
From a philosophical perspective, this is quite an interesting question (this particularly falls within the question of personal identity). According to John Locke, it would be a just punishment, as memories are what define us, and make us who we are, so wiping someone's memories would, according to Locke, make them an entirely different person, and therefore they should not be imprisoned, as they would not be the person who committed the crime.
In my view, however, the wiping of memories, essentially the destruction of someone's identity would be incredibly inhumane, and, from the perspectives of both rehabilitation and retribution in the justice system, would be very much frowned upon, practical issues aside. From the retributive side, they would not believe that the criminal was actually being punished, as he would be allowed to walk free, and his victims would not be given any closure, in addition to not acting as a deterrent (even though there isn't really such a thing as a deterrent in the justice system, but that's a whole other kettle of fish). From the rehabilitative side, it would technically be a form of rehabilitation, as they believe that justice should be about making sure the person doesn't offend again, without using retributive measures. However, rehabilitation is also about treating the offender humanely, and I very much doubt that many people would consider the deletion of a person's memories to be very humane.
Furthermore, this would only really work for people who were actually influenced by their memories to commit crimes, such as people who had a traumatic upbringing. This would not affect people who actually have a psychological condition, such as Antisocial Personality Disorder (from which an estimated 47% of male prisoners and 21% of female prisoners suffer[1]) or other such mental conditions. These conditions can be influenced by genetics (although trauma caused by upbringing can also be a cause of ASPD[2]), as such, the erasure of memories would have little to no effect on whether or not a certain prisoner would re-offend.
Finally, this time from a practical perspective, the area where the brain stores episodic and autobiographical (i.e. events and details about oneself, including memories of childhood trauma) memories is the hippocampus( or Hippocampi, considering there are two of them in the brain), which also plays a role in spatial navigation[3]. This contains most short-term and long-term memories that aren't essential for daily operations, stuff like how to walk and most linguistics are handled elsewhere. However, if an offender were influenced by childhood trauma, then wiping this area would not be effective, as, if this offender were an adult at the time of sentencing, then the traumatic memories would have been moved elsewhere in the brain[4] and they could have caused rewiring in areas such as the Prefrontal Cortex[5] (which handles logic and reasoning). Obviously, modifying the prefrontal cortex in any way could have profound effects on an individual's mental faculties, and it would be inhumane to do so. Additionally, traumatic memories also affect the amygdalae[5], where emotional things are recorded. This part also affects a large number of human behaviours and disorders, such as Post-Traumatic Stress Disorder, or Alcoholism[6], so, again, it would be extremely unethical to modify any of these areas, as it could cause PTSD or alcoholism, among other disorders, so it would be a bad idea to try and affect anything in these areas.
To conclude, from a philosophical (specifically personal identity) point of view, it would be a punishment of sorts, akin to the death penalty, as it would be the termination of one person's existence, only it would lead to the creation of another person as well. However, from both a practical and ethical point of view, I disagree with this idea, and believe we should pursue much more rehabilitative forms of justice, rather than memory deletion.
TL;DR: No.
[1]http://www.thelancet.com/action/showFullTextImages?pii=S0140-6736%2802%2907740-1
[2]http://www.nhs.uk/Conditions/antisocial-personality-disorder/Pages/Introduction.aspx
[3]http://en.wikipedia.org/wiki/Hippocampus#Role_in_spatial_memory_and_navigation
[4]http://en.wikipedia.org/wiki/Hippocampus#Role_in_memory
[5]http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3181836/