No. An Aphasia is defined as
a disturbance of the comprehension and formulation of language caused by dysfunction in specific brain regions. It results from a breakdown of the two-way translation that establishes a correspondence between thoughts and language.
Damasio, A.R. (February 1992). "Aphasia". N Engl J Med. 326 (8): 531–9.
Wikipedia cites that article saying that there needs to be „damage to specific reasons of brain“. Because of this very definition, there is no psychological aphasia, as it then wouldn’t be called aphasia.
Most psychological diseases (dementia as a prime example) have also pathophysiological causes within then brain, so aphasia due to dementia would also be due to brain injury.