Jonathan Ashworth said there should be penalties for social media platforms which allow misinformation to spread, and he urged the Government to bring forward its Online Harms Bill.
Speaking on Sky's Sophy Ridge show, Mr Ashworth said: "I looked on my phone this morning and you can still find stuff on TikTok and so on.
"So we want to work with the Government and find a way of stamping this out. I think it would involve financial penalties."
He said fewer people choosing to take the vaccine due to online misinformation was "the last thing we want".
South Shields man left devastated by fibromyalgia and arthritis sets up new support group to help men talk about their health
Beware of jellyfish - here's what to do if you are stung by one in South Tyneside
'Thousands' may have long Covid in South Tyne
Monkeypox, Covid, flu and hayfever - here's how to tell the difference in the early stages of infection
More than 30 new covid cases in South Tyneside but no more virus-related deaths
Mr Ashworth called on the Government to deal with "some of the dangerous, nonsensical anti-vax stuff that we've seen spreading on social media."
Some of the "poison garbage" conspiracy theories on social media suggested that the vaccine is being developed by "big global business people who want to use it to insert microchips into people", he said.
Ugur Sahin, chief executive of BioNTech, which has announced promising preliminary results of its coronavirus vaccine with Pfizer, said the companies did not see any serious side effects of the jab.
He said the “key side effects” seen so far were a mild to moderate pain in the injection site for a few days, while some of the participants had a mild to moderate fever for a similar period.
“We did not see any other serious side effects which would result in pausing or halting of the study” he told BBC’s The Andrew Marr Show.
“We have now safety data for a proportion of the subjects for more than two months, and we are continuing to collect data for more than two years, to not only see the short and mid-term side effect profile but also the long-term side effect profile.
“But so far the safety profile appears to be absolutely benign.”
Professor Sir Ian Diamond, head of the Office for National Statistics, insisted that a commitment to “openness and transparency” with the presentation of data goes “right across Government”.