A memory module including a row hammer counter chip, a memory system including the same, and a method of operating the memory system are provided. The memory module includes a plurality of data chips each of which is configured to store a data set corresponding to a plurality of burst lengths, and at least one row hammer counter chip including counter memory cells each of which is connected to a word line, among a plurality of word lines, for each of the plurality of data chips, wherein the at least one row hammer counter chip is configured to store in each of the counter memory cells connected to the word line, a number of times the word line is accessed for each of the plurality of data chips during a row hammer monitoring time frame.