Brain systems dealing with multiple meanings of ambiguous stimuli are relatively well studied, while the processing of non-selected meanings is less investigated in the neurophysiological literature and provokes controversy between existing theories. It is debated whether these meanings are actively suppressed and, if yes, whether suppression characterizes any task that involves alternative solutions or only those tasks that emphasize semantic processing or the existence of alternatives. The current functional MRI event-related study used a modified version of the word fragment completion task to reveal brain mechanisms involved in implicit processing of the non-selected solutions of ambiguous fragments. The stimuli were pairs of fragmented adjectives and nouns. Noun fragments could have one or two solutions (resulting in two words with unrelated meanings). Adjective fragments had one solution and created contexts strongly suggesting one solution for ambiguous noun fragments. All fragmented nouns were presented twice during the experiment (with two different adjectives). We revealed that ambiguity resolution was associated with a reduced BOLD signal within several regions related to language processing, including the anterior hippocampi and amygdala and posterior lateral temporal cortex. Obtained findings were interpreted as resulting from brain activity inhibition, which underlies a hypothesized mechanism of suppression of non-selected solutions.