Dan Jarvis said while the infection rate was falling in Sheffield, Barnsley, Doncaster and Rotherham, the situation had not improved enough in other areas for restrictions to be lifted.
The Government will review the tiers next week and will look at factors such as new infection rates in the over 60s, the rate by which cases are rising or falling, the percentage of those tested in local populations with COVID and pressures on the NHS, mainly measured by number of beds occupied.
None of these measures are falling fast enough for the Sheffield City Region to be moved to Tier 2, officials believe.
Currently West Yorkshire, South Yorkshire, Hull and the East Riding are in Tier 3, where indoor mixing is banned and pubs and restaurants are only allowed to operate as takeaways.
North Yorkshire and York are in Tier 2, where pubs and restaurants can offer table service but only serve alcohol alongside a substantial meal. Leaders in York have argued that the city should be placed in Tier 1 as it has the lowest rates in the region and among the lowest in the country.
A formal review of the system will take place on Wednesday December 16 and London may move from Tier 2 to Tier 3 as rates are up in 31 of its 32 boroughs.
Dan Jarvis said: “Four of the five key indicators for areas moving out of Tier 3 are still too high in South Yorkshire.
"Our NHS services remain under massive pressure. Over 600 people are currently in our region’s hospitals with Covid, with more being admitted every single week.
"It is imperative that we avoid a devastating third wave in January and put more lives put at risk – just at the point that a vaccine is being rolled out. It’s likely, therefore, that the Government will decide to keep South Yorkshire in Tier 3 next week.
“I’d reiterate that this decision lies solely with national government. Mayors and Council Leaders are still not being consulted or involved in any meaningful way in the decision-making process. These are decisions taken about us, not with us or by us – which is enormously frustrating and makes a mockery of the Government’s professed commitment to devolution.
“Whatever the Government decide, I’ll continue to work around the clock with our local council leaders, Directors of Public Health and our NHS to ensure that we get out of Tier 3 as quickly and as safely as possible."
Meanwhile, Doncaster’s top health boss says the borough has the highest Covid-19 infection rate in Yorkshire despite falling numbers.
Dr Rupert Suckling, director of public health, said the current infection rate stands at 210 per 100,000 and added the figures were ‘higher than hoped’ when a decision on what tier an area will be.
Labour mayor Mr Jarvis, who is also a Barnsley MP, said extra support was being provided for affected local businesses through the Sheffield City Region's Additional Restrictions Grant.
He added: "I’d urge eligible businesses to apply for those funds, and I’ll keep on fighting for the additional support and resources our businesses, supply chains and regional economy needs to weather the storm of this awful disease.
“There is now light at the end of the tunnel, with a vaccine already being rolled our across the country. But until we can ensure enough people have received the vaccine, the threat remains.
"We must all adhere to the guidance and do our bit to save lives and livelihoods. We are on the home stretch, but we must ensure that we all make it to the finish line.”
Greater Manchester has a "strong case" to come out of Tier 3 restrictions when they are reviewed next week, the region's mayor said.
Andy Burnham said the region's current rates of infection compare favourably with those of Liverpool and London when those cities were placed in Tier 2.