How can I give the minimum permission?

It is not only one stored procedure that the user needs permission to. There are at least two dozen. Do I need to grant permission to each of them? Also, I would like to make sure this wouldn't give the user access to any other object in the DB?  

>> It is not only one stored procedure that the user needs permission to. There are at least two dozen

Then you need to GRANT execute permission to all the required stored procedures.
In the meanwhile, why are you having user stored procedures in master database which is not a recommended approach at all.

>> Also, I would like to make sure this wouldn't give the user access to any other object in the DB?  

Revoke Public role and disable guest account.
Now granting CONNECT permissions to only required database and EXECUTE privilege on required stored procedures would suffice (it won't give access to other objects for sure)

Thank you rrjegan17! This was exactly what I wanted to do. But I have an external vendor that requested to have their stored procedures in the master db.  Their reason I think is they use a third party tool that apparently converts their existing Access based DB to SQL.  They never re-wrote their code so they are translating everything.   So now I have to figure out how to give only an execute permission without even giving public role to this user. (Is this even possible?)

I guess you have answered my question. I posted comment with refreshing the browser. I will try that. Thanks much!