The PHB and basic rules state about falling:
At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.
The bullywug's statblock (MM, p. 35) mentions:
Standing Leap. The bullywug’s long jump is up to 20 feet and its high jump is up to 10 feet, with or without a running start.
So if a bullywug high-jumps as high as it can, would it take 1d6 damage and fall prone?