Military engineering is the practice of building and designing military works and maintaining lines of military transport and Communications.It is not a course where you work as an army officer.So, you don't have to appear any fittness exam to become a military engineer. Your job includes building devices required in warfare.During the peacetime, these engineersnare also engaged in the non-military construction tasks such as flood control, etc in some countries of the world.
In India,College of military Engineering ,Pune is one of the best colleges for those to want to become a military engineer. They provide the following courses:
UG courses leading to the B.Tech (Bachelor of Technology) degree – 4 years durationin civil, electrical and mechanical engineering
PG courses leading to the M.Tech (Master of Technology) degree – 3 years duration in structural engineering.
Then you have to intership in this field tp increase your knowledge.
After the completion of full bachelore's course youhave to give Professional engineer exam which will get you your license as an engineer and can apply in army as military engineer.

NO dear, there is not having any fitness test to get admission in the college of military engineering. Eligibility for B.Tech course whose duration is 4 year. The aspirant who is 10+2 passed with physics,maths and chemistry subject and have secured a minimum 70% marks and the Entrance exam held by the University should be qualified.

All the best dear Kaushal