Depends on your skill level.  But you can turn any given guitar skill into a (presumably) picking hand exercises by simplifying the fretting hand part.

If you working on strumming, then just play the open strings, or play a simplified chord that doesn't involve your middle finger.  For example, this tutorial in GF1.

https://www.guitartricks.com/lesson/31247

Anders plays 2 very simple voicings of E minor & G major only using his ring finger to fret.  The main focus is strumming.  You could do more advanced strumming patterns with those, or you could work on arpeggiating (play the chord notes rhythmically separated).

Caren has some good advice in this tutorial on strumming.  Just don't play the chords until you are healed.

https://www.guitartricks.com/tutorial/1408

Mike did a good one on rock style strumming.  And on this one you can modify the parts to only using power chords with your index & pinky.

https://www.guitartricks.com/tutorial/2902

These tutorials are aimed at learning the basics of rock style picking & strumming.  You can leave off the chords, or modify them to one or two finger power chords.

https://www.guitartricks.com/tutorial/1492

https://www.guitartricks.com/tutorial/1593

If you are looking for more advanced exercises, I have some advanced rock picking exercises & some classical fingerpicking exercises.  You can modify these to leaving out your middle finger, or just leave off fretted notes completely & work on the picking hand.

https://www.guitartricks.com/tutorial/287/

https://www.guitartricks.com/tutorial/1031/

https://www.guitartricks.com/tutorial/1085/

Hope that helps & your finger heals soon!