This is a very interesting scenario. The money was borrowed by the brother of a staff member from your branch. It was not borrowed by a staff member. However, it is likely that the brother came in touch with the customer through the staff member and that the request was sent by the staff member to the customer. If he has done so, or if he has used any incitement, offer of additional service, or illegal gratification to convince the customer to give the loan, then he is open to action from your side. In fact, he may be liable to criminal prosecution if any of the above involves cheating/misrepresentation to the client.
Review Standing Orders and Employment Terms
You need to check your standing orders, terms of employment, and documents signed by the employee when he joined. There will probably be some rules against this. You should immediately take up the matter with the HR department and with your vigilance department. They may want him suspended pending inquiry and settlement of the matter as it is a sensitive subject.
Escalate to Senior Management
Further, given that this involves customer goodwill and trust, you need to escalate this upwards to your operations head/zonal head and take action based on their recommendation.
Personally, I would like such an employee removed from my organization as he cannot be trusted. In a bank, all employment is on "Uberrima Fides," which means of utmost good faith. You cannot have an employee who is involved in any subterfuge as he may indulge in fraud using the bank's name/property or his position in the bank.
Regards.