The Livingston manager felt a ‘circuit-breaker’ was required in the face of the Omicron variant, which has led to the highest recorded number of cases in one day since the pandemic started.
In England more than ten games are already off. That includes Manchester United' s match against Brighton on Saturday and last night’s game between Leicester and Tottenham.
The Scottish FA and the SPFL are consulting with their member clubs over tightened Covid protocols in the wake of a rise in cases linked to the Omicron variant.
As it stands, all matches – including Sunday's Premier Sports Cup final between Hibs and Celtic – will go ahead.
Neilson, however, doesn’t think it’s right to take football off the table at this moment in time with so many supporters needing the sense of community during the festive period.
Speaking ahead of his team's trip to face Dundee on Saturday, the Hearts boss said: "I don't think we need that at the moment. We've got the break coming up in January so that hopefully will give us a chance to see it out a little bit.
"One of the things you've got to remember with football is people's lives revolve around it and they need it over this festive period, hence the reason there are a lot of games.
"We have an obligation to make sure we don't put ourselves in areas we're going to cause ourselves problems but also to make sure we put games on.
"We just need to make sure we keep our house in order and the players and staff follow the protocols and look after themselves, and hopefully we can get through this again.
"Touch wood, we've managed to keep things negative but sometimes it can be outwith your control so we just need to keep following the procedures."
South of the border, the Premier League is resisting calls to suspend all matches this weekend despite a raft of Covid-related postponements in the last 48 hours.
Manchester United's match against Brighton on Saturday is the latest to have been called off due to the number of Covid-19 cases in the Red Devils camp, with Thursday's game between Leicester and Tottenham also postponed.
The number of postponed weekend matches across England's top four divisions reached double figures by 3pm on Thursday, with the EFL announcing stricter Covid protocols including increased testing.
United are understood to have had only nine players available because of Covid and other injuries for Tuesday's game against Brentford, which was called off late on Monday night, and just seven for the Saturday lunchtime match against Brighton at Old Trafford.
Brentford manager Thomas Frank called for all of the weekend's top-flight matches to be postponed, with the highly-transmissible Omicron variant wreaking havoc with the schedule, but the league is currently intending to play as many games as possible.