The Scot, 42, had offered to resign if the team did not get a "positive result" at Braintree on Saturday.
Following the 1-1 draw with the Iron, McNamara told BBC Radio York he would speak to chairman Jason McGill about his future.
The club said in a statement: "The chairman has asked Jackie to train and prepare the team until a suitable candidate has been determined."
They added that they expected the process to appoint a new boss to take a fortnight.
McNamara, who won 33 caps for Scotland during his playing career, was appointed manager of the Bootham Crescent side in November 2015 but was unable to prevent them from being relegated from League Two.
They started this season slowly and a humiliating 6-1 defeat by previously winless Guiseley on Tuesday 4 October prompted the former Scotland international to offer to quit.
The ex-Partick Thistle and Dundee United boss leaves the Minstermen in 19th in the National League, three points above the relegation zone.
They face Curzon Ashton in the fourth qualifying round of the FA Cup on Saturday before returning to league action with a home match against Chester on 22 October.
York City boss Jackie McNamara is to step down in the next two weeks.