Yours is a tricky situation. On the one side you need to claim shift allowance and on the another cannot antagonise your manager too.
Next time when the topic comes for discussion then tell him that since this issue is related to the payment, it is beyond scope of your authority. Therefore, it is better if he calls the meeting of all the subordinates who report to you. Let him "tell" them not to claim for the shift allowance. While in the meeting if possible let someone record voice of the Manager surreptitiously on his/her mobile. Preserve the audio file securely.
Thereafter, take a collective decision. Your team will have option of abiding with what your Manager has said. The section option is to defy the manager. If the collective decision is to go against what manager has said then let all the team members together submit the application to the MD of the company. However, route the application through HR.
General comments: - This is a general scenario in MSMEs. We do now the the exact nature of the case but either of the two things are obvious. One is that Manager is under to pressure to control the operational cost and for this he is pressuring his team members give a week's shift allowance every month. The second could be top leadership himself might have told Manager to pass on the instruction. But to avoid the direct exposure, the leadership could be shooting from the shoulder of the manager. In either case, such instances vitiate the culture of the company. With the vitiated culture, a phenomenal growth is a remote possibility.
In addition to Dinesh Sir's advise, there is still a big WHY here. That why exactly he is stopping you from claiming shift allowance and that also only for one week. Is it that, for one week your team work in general shift which does not have shift allowance. If this is not the case you can ask him that you will claim what you should rightfully and let the management decide how much to pay or else ask him to provide circular for the same. Hope that will solve your issue