Green’s Dictionary of Slang

(US) a wedding that is forced on the groom through his girlfriend’s (soon to be bride’s) pregnancy.

1981		(con. 1920s) P. Crosbie Your Dinner’s Poured Out! 32: Fights between women [...] consisted of a good deal of hand-slapping and repetitive name-calling, culminating in a question like ‘Who was it had a military weddin?’ This was the signal for real action.
1992		W.G. Cahan No Stranger to Tears 81: The four of us were often called upon as witnesses for a military wedding. ‘Military’ in both senses of that word: it was of the shotgun variety. This usually involved a pregnant nurse or WAC.
2004		J. Dunn Willis Ave 57: It was a military wedding. The very pregnant Angie’s father showed up with a shotgun.