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I allowed my friend living in different province to work in my SIN number. Will that be a problem for me in future when I apply for PR. I am on work permit right now

Not really sure as to how it will affect your future PR app but one thing i do know is if in the event your friend's employer will suspect or become aware of it, they have the obligation to report it to the relevant authorities as it is a violation of the income tax act.
 
I allowed my friend living in different province to work in my SIN number. Will that be a problem for me in future when I apply for PR. I am on work permit right now

It’s a crime. Yes it will cause you lots of problems and will also create tax problems for you.
 
Its tax fraud, and it is a federal crime. You can't exactly apply for PR while in prison.