It follows revelations today that one of Mr Matheson's most senior civil servants sought to delay the publication of a report into the Scottish Police Authority by the police watchdog.
E-mails published by the Sunday Post today show that Scottish Government official Don McGillivray suggested that Police Investigations and Review Commissioner (PIRC) Kate Frame could hold back publication of the report into SPA complaints.
It comes after former SPA chair Andrew Flanagan told MSPs last week he felt he had no choice but to block the planned return to work of sidelined Police Constable Phil Gormley after Mr Matheson intervened in the process.
Scottish Conservative justice spokesman Liam Kerr said today: “These new revelations show that the SNP Government’s meddling in police matters is endemic, both at the SPA and now with the PIRC.
“Michael Matheson's department has torn up the rule book that is supposed to protect the independence of our police service, and as such the Scottish public can no longer have confidence in him.
"Simply put, the best course of action would be for him to resign."
Labour will demand the Justice Secretary comes to Parliament this week to justify these actions in a Holyrood statement.
“This is a shocking revelation of attempted government interference in a supposedly independent investigation into the SPA, which in turn is supposed to be independent of ministers," Mr Johnson said.
"The independence of policing is a fundamental point of principle and of law.
“Michael Matheson’s department has treated operational independence of policing with contempt with its repeated interventions.
“The Justice Secretary has already misled Parliament about his dealings with the SPA, calling into question his position, now we find his department has tried to interfere with a PIRC investigation as well.
“As Cabinet Secretary for Justice, Michael Matheson must take responsibility for his actions and those of his department. This is just the latest evidence is a series of actions compromising the independence of the bodies that run policing in Scotland. It is hard to conceive how Mr Matheson can justify these actions, but Labour will be demanding he comes to Parliament and attempts to, and if he cannot, he must resign."
"PIRC is an independent body and has made clear there has been no interference in the publication of this report. The Scottish Government has no role in either the timing or content of its reports.
"It is part of the mormal role of the sponsorship function to support public bodies to consider their role int eh wider context of public services."