I doubt if a thing like this would be possible without the use of external influences, because there is nothing impossible in today's world. Maybe scientists are coming up or have came up with substances that can help in blotting out what is in one's mind. But realistically, without the use of something like this, I don't think it would naturally be possible to not be able to use one's memories.
More significantly, memory is the most important part of the human brain which helps in keeping records of what has happened from the day we were born till the day we die. And if anything happens to it, there won't be anything we can hold on to. We won't be able remember the slightest things like names of our relatives, friends we once had, places we once visited, etc.
From what I was thought that human memory can only be erased when there is serious fatal accident. And if the human brain is severely affected, there could the condition called amnesia.