Hello Aspirant,
No, NEET is not necessary for MNS. I have wrote the selection procedure of last year. Check it out

MNS 2021 Selection Procedure

As you know, only female candidates are eligible to apply for the Military Nursing Service. To get selected in the MNS, One will need to clear the three phases of the selection process which consists of:

• Written Examination
• Personal Interview
• Medical Exam etc

The Written Exam of MNS is the toughest phase of selection. The weightage of selection is based on that. All the candidates who would clear the written exam will proceed for the Personal Interview and then Medical Exam which is conducted by the Military Doctors at the Military Hospital.

Hope this helps.

All the best