Looks like there is a pine wood frame behind/alongside the MDF edge where the MDF itself has split? And the way you've mounted the door with that hinge means the screws don't appear to have gone into the pine frame work for the MDF; but into the MDF edge only? Did you drill pilot holes for the screws prior to actually screwing them in; just a wee 3mm pilot hole would suffice? MDF really doesn't like screws going in without a suitable pilot hole.
Edge screwing even with a pilot hole into MDF isn't the best, especially if the attachment (e.g. a door) is putting stress on it. - unless it's a decent thickness, say 18mm at least - preferably 25mm; and even then the correct type of hinge will make a deal of difference. I suspect the MDF is about 15-18mm. If the lower then not really best choice to mount a hinge one, unless the hinge is also mounted onto something more solid - e.g real timber... - as well; and if the higher then still not the ideal the way to go/hinge to use in your installation as shown.
As already suggested, glue and clamp the MDF tight until it's set. Then "carefully" drill out a hole in the edge to allow a suitable plastic plug to go in; ensure you use the correct drill bit size required for the plug; and in the right location of course. Tap the plug(s) fully home and then simply screw the hinge back in place (screws will likely/ought to be a wee longer than previous). Glueing the plugs may not be required... - if one uses a soft/flexible plug (e.g. Fischer or similar) rather than say the more rigid plaslugs/rawplugs. I prefer Fischer (they're more flexible) plugs which usually come in boxes and clearly show the correct pilot bit to use for the plug, rather than the harder/more solid plasplugs... Screwfix have Fischer in boxes and baggies of similar (the latter usually don't indicate the drill bit size, but a test run on a scrap of wood will soon tell you what size wood bit to use ((brad point bit of course).
The white dowel hinge plugs etc suggested above wouldn't be my first choice; they will require a thicker edge to work with safely/securely; and you'd need longer screws...
But as suggested already a better/different choice of hinge would be the way to go anon; one which allows more fixing to the pine frame work?
Something like this perhaps:
https://tinyurl.com/mrj7takz
There are many variations on this type of hinge; so it's useful to go view them them and see which would work to your preferences. And as suggested by others above, perhaps even make a feature of the hinge rather than hide it away with the type of hinge you've used thus far?
If you have decent SF, B&Q, etc.; even better say a Champions Timber locally, go have a look see and you'll find something more suited for the job. And as just above drill pilot hole for the additional/new screw appropriate for the screw used - 3mm at least if into pine; and for the MDF you may need to go to 4mm - but try that on a scrap of MDF first to determine the best pilto bit there..
Ideally the hinge would/should be more securely mounted onto the pine frame work as well partially onto the edge of the MDF panel.
Equally you may find it wise(r) to reposition the duff/loose hinge (perhaps both) slightly even after the glue/clamp process; regardless of what type of hinge(s) you settle for?
However you resolve this, remember that the door is putting a deal of torque/stress on the hinge mounting..., so it's essential that the screws are well and truly applied.
