Both clubs have reported cases of COVID-19, and so will unable to play in their scheduled ties against West Bridgford and Whitley Bay respectively.
A Lincoln United club statement said: “We have been working closely with Public and Environmental Health in order to ensure the club follows guidelines to contain the spread of the virus, prioritise health and ensure our facilities are safe to use.
“The club can confirm there have been no further confirmed Covid-19 cases at the club since the initial outbreak of eight players, and stress the decision to not play in this Saturday's fixture, is following the advice from Public and Environmental Health, and not due to any further positive tests within the club.
"Due to the nature of the FA Cup, the game is unable to be postponed, meaning the men's first team are out of this season's competition."
Dunston have also acted swiftly after learning of a positive test within their squad, contacting Public Health England and issuing instructions to all persons that have been in full contact with those affected that they must self-isolate for 14 days.
A third Northern Premier League club, Carlton Town, will progress to the next round of the FA Cup after their scheduled opponents Oadby Town were forced to withdraw due to a COVID-19 outbreak.