Put your menu in a block. In the block, select Show if the following PHP code returns TRUE (PHP-mode, experts only) and check the UID and return false for the UID you want to block.
It would be helpful for you to have Devel. If it was me, I would also have a specific role, assign those users roles and just block the role and that way you can block certain roles.
Put your menu in a block.
Put your menu in a block. In the block, select Show if the following PHP code returns TRUE (PHP-mode, experts only) and check the UID and return false for the UID you want to block.
It would be helpful for you to have Devel. If it was me, I would also have a specific role, assign those users roles and just block the role and that way you can block certain roles.