TOKYO—Japan's nuclear crisis showed signs of spinning out of control Tuesday, after officials reported a third explosion and warned of possible damage to a critical reactor container at the troubled Fukushima Daiichi nuclear-power complex.

Tuesday's explosion at the No. 2 reactor in the Fukushima complex, 150 miles north of Tokyo, for the first time raised the possibility that the key containment structure of the unit, which protects the reactor vessel and keeps dangerous radioactive materials from leaking out, had been damaged....