Full duplex (FD) systems suffer from very high hardware cost and high power consumption to mitigate the self-interference (SI) in the analog domain. Moreover, in millimeter wave (mmWave) they rely on hybrid beamforming (HYBF) as a signal processing tool to partially deal with the SI, which presents many drawbacks such as high insertion loss and high power consumption. This article proposes the use of near-field (NF-) IRSs for FD systems with the objective to solve the aforementioned issues cost-efficiently. Namely, we propose to truncate the analog/hybrid beamforming stage of the mmWave FD systems and compensate it with an NF-IRS, to simultaneously and smartly control the uplink (UL) and downlink (DL) channels, while assisting in shaping the SI channel: this to obtain very strong passive SI cancellation. A novel joint active and passive beamforming design for the weighted sum-rate (WSR) maximization of a NF-IRS-assisted mmWave point-to-point FD system is presented. Results show that the proposed solution fully reaps the benefits of the IRSs only when they operate in the NF, which leads to considerably higher gains compared to the conventional massive MIMO (mMIMO) mmWave FD and half duplex (HD) systems.