Which is correct: To "take a medical leave" or to "take medical leave"?

Solution 1:

When used as part of the phrase leave of absence, it's common to use an 'a' before leave. It can also be pluralized to leaves of absence if need be. E.g.

Did you hear Bob had to take a medical leave of absence?

Mary is out again. That makes five leaves of absence in as many years.

Solution 2:

Both constructions are correct. The different usages arise from leave's status as both a noun, and a portion of the mostly archaic verb phrase to take leave.

When it's used in the phrase, take a medical leave, leave is acting as a noun, and it's entirely akin to the word vacation or break. Medical acts an adjective describing the noun. As a noun, leave usually takes the preposition on, when it's used as an indirect object.

When it's used in the phrase, take medical leave, take leave is acting as a verb phrase, meaning "to depart," and medical is an adverb describing how the leave was taken.

Here are some usages of leave as a noun:

I've been on leave for 6 months; no one has noticed and phoned me to return just yet!

How long can the soldiers stay on leave? The Germans have just crossed the Maginot Line.

I gave PFC Downey and Lance Corporal Dawson leave to do as they liked; I certainly didn't order the Code Red.

Here are some usages of to take leave as an archaic verb:

I took leave of my guests after making the requisite excuses, and prepared my pistols in the drawing room.

When shall we take leave of dreary England and embark to the warm beaches of the Azores?

I have taken leave of my employment with Mr. Holmes and wish to pursue the happiest of marriages with you, my dear Ms. Morstan.