We develop a nonequilibrium increment method to compute the Rényi entanglement entropy and investigate its scaling behavior at the deconfined critical (DQC) point via large-scale quantum Monte Carlo simulations. To benchmark the method, we first show that, at a conformally invariant critical point of O(3) transition, the entanglement entropy exhibits universal scaling behavior of area law with logarithmic corner corrections, and the obtained correction exponent represents the current central charge of the critical theory. Then we move on to the deconfined quantum critical point, where we still observe similar scaling behavior, but with a very different exponent. Namely, the corner correction exponent is found to be negative. Such a negative exponent is in sharp contrast with the positivity condition of the Rényi entanglement entropy, which holds for unitary conformal field theories (CFTs). Our results unambiguously reveal fundamental differences between DQC and quantum critical points described by unitary CFTs.