Language comprehension relies on a multitude of domain-general and domain-specific cognitive operations. This study asks whether the domain-specific grammatical computations are obligatorily invoked whenever we process linguistic inputs. Using fMRI and three complementary measures of neural activity, we tested how domain-general and domain-specific demands of single word comprehension engage cortical language networks, and whether the left frontotemporal network (commonly taken to support domain-specific grammatical computations) automatically processes grammatical information present in inflectionally complex words. In a natural listening task, participants were presented with words that manipulated domain-general and domain-specific processing demands in a 2 × 2 manner. The results showed that only domain-general demands of mapping words onto their representations consistently engaged the language processing system during single word comprehension, triggering increased activity and connectivity in bilateral frontotemporal regions, as well as bilateral encoding across multivoxel activity patterns. In contrast, inflectional complexity failed to activate left frontotemporal regions in this task, implying that domain-specific grammatical processing in the left hemisphere is not automatically triggered when the processing context does not specifically require such analysis. This suggests that cortical computations invoked by language processing critically depend on the current communicative goals and demands, underlining the importance of domain-general processes in language comprehension, and arguing against the strong domain-specific view of the LH network function.