There's just one thing you're missing. Especially, if you're using InnoDB, is you want to explicitly add an ORDER BY clause in your SELECT statement to ensure you're inserting rows in primary key (clustered index) order:
INSERT INTO product_backup SELECT * FROM product ORDER BY product_id
Consider removing secondary indexes on the backup table if they're not needed. This will also save some load on the server.
Finally, if you are using InnoDB, reduce the number of row locks that are required and just explicitly lock both tables:
LOCK TABLES product_backup WRITE;
LOCK TABLES product READ;
INSERT INTO product_backup SELECT * FROM product ORDER BY product_id;
UNLOCK TABLES;
The locking stuff probably won't make a huge difference, as row locking is very fast (though not as fast as table locks), but since you asked.