Diagnosis
The defrost drain is clogged. When the freezer automatically defrosts, the meltwater is supposed to drain down a tube into a pan at the bottom. If that drain hole (in the back of the freezer compartment) gets plugged with ice or gunk, the water backs up and leaks into the fridge.
How to Fix It
1) Unplug the fridge. 2) Remove everything from the freezer and locate the drain hole on the back wall, near the bottom. You'll likely see ice covering it. 3) The safest fix is to melt that ice. Use a turkey baster or syringe to pour warm (not boiling) water into the drain hole. You can also use a hairdryer on low to gently melt the ice blockage. 4) Once it's clear, pour a little warm water down the hole to ensure it flows freely to the drain pan below.
If That Didn't Work
If the drain clears but the problem quickly returns, the drain tube itself might be frozen its entire length due to a failing defrost heater. This is a more serious repair, as the heater or defrost thermostat may need replacement to prevent recurring clogs.
Heads Up
Don't use anything sharp like a wire hanger to clear the drain. You could puncture the drain line, which is a much more expensive fix. Patience and warm water are your best tools here.