Patients with COVID-19 may experience various neurological conditions, including cognitive impairment, encephalitis, and stroke. This is particularly significant in individuals who already have Alzheimer's disease (AD), as the cognitive impairments can be more pronounced in these cases. However, the extent and underlying mechanisms of cognitive impairments in COVID-19-infected AD patients have yet to be fully investigated through clinical and neurophysiological approaches. This study included a total of 77 AD patients. Cognitive functions were assessed using neuropsychiatric scales for all participants, and plasma biomarkers of amyloid protein and tau protein were measured in a subset of 25 participants. To investigate the changes in functional brain connectivity induced by COVID-19 infection, a cross-sectional neuroimaging design was conducted involving a subset of 37 AD patients, including a control group of 18 AD participants without COVID-19 infection and a COVID-19 group consisting of 19 AD participants. For the 77 AD patients between the stages of pre and post COVID-19 infection, there were significant differences in cognitive function and psychobehavioral symptoms on the Montreal Scale (MoCA), the neuropsychiatric inventory (NPI), the clinician's global impression of change (CIBIC-Plus), and the activity of daily living scale (ADL). The COVID-19 infection significantly decreased the plasma biomarker level of Aβ42 and increased the plasma p-tau181 level in AD patients. The COVID-19-infected AD patients show decreased local coherence (LCOR) in the anterior middle temporal gyrus and decreased global correlation (GCOR) in the precuneus and the medial prefrontal cortex. The findings suggest clinical, cognitive, and neural alterations following COVID-19 infection in AD patients and emphasize the need for close monitoring of symptoms in AD patients who have had COVID-19 and further exploration of the underlying mechanisms.