Amyotrophic lateral sclerosis (ALS) primarily affects motor and speech abilities. In addition, cognitive functions are impaired in a subset of patients. There is a need to establish an eye movement-based method of neuropsychological assessment suitable for severely physically impaired patients with ALS. Forty-eight ALS patients and thirty-two healthy controls matched for age, sex and education performed a hand and speech motor-free version of the Raven's coloured progressive matrices (CPM) and the D2-test which had been especially adapted for eye-tracking control. Data were compared to a classical motor-dependent paper-pencil version. The association of parameters of the eye-tracking and the paper-pencil version of the tests and the differences between and within groups were studied. Subjects presented similar results in the eye-tracking and the corresponding paper-pencil versions of the CPM and D2-test: a correlation between performance accuracy for the CPM was observed for ALS patients (p < 0.001) and controls (p < 0.001) and in the D2-test for controls (p = 0.048), whereas this correlation did not reach statistical significance for ALS patients (p = 0.096). ALS patients performed worse in the CPM than controls in the eye-tracking (p = 0.053) and the paper-pencil version (p = 0.042). Most importantly, eye-tracking versions of the CPM (p < 0.001) and the D2-test (p = 0.024) reliably distinguished between more and less cognitively impaired patients. Eye-tracking-based neuropsychological testing is a promising approach for assessing cognitive deficits in patients who are unable to speak or write such as patients with severe ALS.