Northern said a number of front-line members of staff have tested positive for Covid-19, while others are being forced to self-isolate.
The company said there would be disruptions across the weekend, with Cumrbia being the worst affected area.
Chris Jackson regional director at Northern, said: “A high proportion of staff based at Barrow and Workington have been instructed to self-isolate. This has exacerbated issues we were already experiencing in the region following an increase in the number of employees who have either tested positive for COVID-19 or have had to enter a period of self-isolation.
“Many of these colleagues are drivers and conductors and, as such, we are left with no option but to cancel some services this week in Cumbria and north Lancashire.
“We are doing all we can to provide the best possible service for customers in extremely difficult circumstances and, where we are not able to run rail services, we will have replacement buses on standby to get our customers where they need to be.”
Northern is also advising customers to expect busier services on Saturday night, particularly in larger towns and cities, following the Euro 2020 quarter final between England and Ukraine.
The rail operator is asking those planning to travel on Saturday night to think carefully about their journeys and not to wait until the last train home.
Mr Jackson added: “Of course, many people will want to support England and will be travelling to pubs and bars to watch the match.
“With kick off at 8pm, that only leaves a handful of trains on our key routes after the match to get people home and we’re asking our customers to plan ahead and to use all available services. We’ll have buses on standby in many places to assist, but customers can help by staggering their journeys and not all waiting for the last train home.”