There’s two examples of major straight to minor I can think of from jazz. You might want to check them out.
The first, which fits your description best, is the opening four bars of the chords to the A section of ‘On Green Dolphin Street’. In concert C, it’s:
Cmaj7 | Cmaj7 | Cm7 | Cm7 | ...
The second is in the tune ‘Alone Together’. The A section begins in D minor, but moves to D major by the end, and during the transition to the second A section, the D major goes directly to a D minor chord.
In both of the cases above, I don’t think it serves as a functional progression though. It’s just, colour.
As coconochao mentions, the IV - iv - I ending is a common example of direct major-minor. I believe this is a form of Modal Interchange, a different way of approaching chord progressions. I personally like to use it whilst improvising on jazz ballads.
As for whether it sounds odd... I believe that’s just a matter of how accustomed to it your ears are. I like it because it sounds different from conventional functional progressions.
Additional thought: Just realized these are all major to minor, not minor to major. I don’t know why that it. Maybe our ears prefer going to flatter keys over going to sharper keys. (Minor is just major with more flats.)
Additional additional thought:
Perhaps it’s because we associate tension with going up (getting brighter, thus sharper) and resolution with going down (getting darker, hence flatter).