Working on the assumption that it was 3 1/2 inch floppy disk, there are varying degrees of "open".
The easiest part of a floppy disk for a three-year-old to remove would be the sprung metal shutter. (It's probably the most entertaining part for someone to start playing with in the first place.)
The shutter's purpose is to protect the disk surface from dust, dirt, and fingerprints. Older 5 1/4 and 8 inch disks had no shutter, and were stored in a sleeve instead. The shutter is pushed to the side when the disk is inserted, to let the drive's heads read the magnetic surface inside.
If the shutter is bent slightly, so that the faces are "lifting up" from the case, this can be a problem: the shutter may catch on the floppy drive's door when ejecting the disk, resulting in a disk stuck in the drive. (Such a disk can usually be prised out by lifting the door clear of the bent shutter.)
If the shutter has been removed completely, then it will cause no problem in the disk drive. The heads will be able to access the magnetic surface with no obstruction at all. It would, however be a good idea to back up the data stored on the disk, as it will now be more vulnerable to ingress of dirt and dust through the open hole.