Morton was only confirmed as "permanent" manager in May after leading the Minstermen to Conference safety in a three-month stint as caretaker.
In a statement they said they had “reluctantly taken the decision”.
His assistant, Tony McMahon has been put in charge.
York-born Morton's final game was a 3-1 defeat to Rochdale.
Last week the club signed Dan Batty, Jack Stott, Kai Kennedy and Rory Watson.
Morton, a former Tadcaster Albion manager who also coached in Leeds United's academy, was put in temporary charge after initially joining as assistant to Dave Webb in December.
Webb came in to replace the sacked John Askey, but was unable to take charge of his initial games because of Covid-19. He was sacked after just 11 games.
Morton was named as interim in February, and in March it was confirmed he would see the team through until the end of the campaign. He led the newly-promoted side to 19th but they currently sit 23rd in the division after three draws and three losses.