It had been agreed McCarthy would leave at the end of the season, but the 59-year-old walked away following Ipswich's 1-0 home win over Barnsley.
McCarthy held a brief press conference after the match in which he was asked a question about the fans' negative reaction to Barry Cotter's substitution, to which he replied: 'That was a disgraceful reaction, but listen I won't have to listen to it again because that's my last game, I'm out of here.'
With that, McCarthy banged the desk in front of him and left the room, before his departure was officially announced by the club shortly afterwards.
Evans has told the club's website that he will take his time over an appointment and that it is unlikely a new man will be in place before the end of the season.
'Appointing a manager is one of the most important - if not the most important - decision an owner of a football club will make,' said Evans.
'I have started the process, but I will take all the time I need to find the right person.
'A lot can happen around the end of the season with managers, so I want to be in the best position I can be before making an appointment.
'I can't rule it out completely, but I don't envisage confirming our next manager until the season is finished.'
Terry Connor also departed along with McCarthy, so Bryan Klug will take charge of Ipswich's remaining four matches this campaign.