A ZeroDivisionError in Python arises when a division or modulo operation involves a denominator or divisor of zero, as division by zero is mathematically undefined. To prevent this error, one can use conditional statements to check if the denominator is zero before performing the division, or employ try-except blocks to handle the error gracefully if the denominator's value is unpredictable. The error can be effectively managed using tools like Rollbar, which automates error monitoring and triaging, thus simplifying the process of fixing Python errors and enhancing confidence during code deployment.