Yes, a good old NE555 will do the job I suspect.
And the great thing is it only has a few legs.
Well, how can I have resisted with you asking how you could do this 'without' an Arduino?
There are many general forums for electronics if you prefer not to use an Arduino.
Using an Arduino will allow you many great and wonderful benefits such as adding shields and extra nu-necessary hardware but that make your project handsomely more geeky by being able to tweet, beep, and post to the web that you are running your motor.
You could count how many times the motor has started, how many times in the past hour or day, even pre-program it for the future, wow!
You can even read the current the motor consumes and do something with that too if you wish.
To do this without an Arduino, say with valves or a NE555 might prove difficult to say the least.
Oh, yes, I am cheeky today, forgive me,
rockwallaby