Summary: For an integer \(k\geq 2\), let \((F_{n}^{(k)})_{n}\) be the \(k\)-Fibonacci sequence which starts with \(0,\ldots ,0,1\) (\(k\) terms) and each term afterwards is the sum of the \(k\) preceding terms. In this paper, we find all \(k\)-Fibonacci numbers which are Mersenne numbers, i.e., \(k\)-Fibonacci numbers that are equal to 1 less than a power of 2. As a consequence, for each fixed \(k\), we prove that there is at most one Mersenne prime in \((F_{n}^{(k)})_{n}\).