Work and Pensions Secretary Theresa Coffey blamed an "IT failure" within Public Health England for a delay in the reporting of 15,841 COVID-19 cases in England.
Ministers have been accused of overseeing a "shambolic" system since the glitch was acknowledged.
It means the total number of coronavirus infections reported over the coming days will include some additional cases from between 25 September and 2 October.
Asked whether others might have been infected with COVID-19 due to the NHS Test and Trace scheme not being aware of the nearly 16,000 cases, Ms Coffey told Sky News: "There may well be.
"I've been made aware that probably the majority of that [contact-tracing] has happened in the latest element of the week, in the last couple of days.
"So it's important that we act quickly, and PHE is acting quickly, to see whether or not people are required to self-isolate.
"Because I do recognise that not quite everybody going through the regime will be identified by the test and trace regime to undertake that further self-isolation."
Asked whether the government would be issuing an apology over the issue, Ms Coffey pointed towards Health Secretary Matt Hancock's expected appearance in the House of Commons later on Monday.
In an earlier broadcast interview, Ms Coffey was unable to say how many close contacts of coronavirus cases were not contacted because of the system failure.
"I'm afraid I just don't have that information," she told BBC Breakfast.
Asked if they have now been contacted, she said: "I know that people who had the initial results have all been contacted, I don't know the answer to that question."
Labour MP Bridget Phillipson, the shadow chief secretary to the Treasury, accused ministers of overseeing a "shambolic" system.
"Test, trace and isolate just isn't working," she told Sky News.
Fellow Labour frontbencher Lucy Powell, the Manchester Central MP and a shadow business minister, said it was "very concerning" that infection rates had been revised upwards in Greater Manchester following the discovery of the computer glitch.
"Local understanding of what lies behind this increase is critical before we see ever more stringent restrictions imposed on us," she posted on Twitter.
"We've already been living under local restrictions longer (over 2 months) than most places."
Public Health England said on Sunday the people involved all received their test results and those who tested positive were advised to self-isolate.
Joint medical director Dr Susan Hopkins told Sky News: "There's no delay in people receiving their test results.
"The delays are in reporting to the dashboard and to the public and there's been a delay in contact tracing initiation.
"Public Health England apologise that this occurred and have put in place steps to prevent this happening again."