Police said they handed out three fixed penalty notices to the individuals on Sunday morning.
Officers from Newport Safer Neighbourhood Team, part of West Mercia Police, issued the fines.
A spokesperson from Newport SNT said: "PCSO Liston has completed some early morning wakeup calls and handed out three Covid tickets to individuals who figured it was okay to have a sleepover during a pandemic."
The cost of a first offence of breaching coronavirus restrictions is £200 – which is lowered to £100 if paid within 14 days – and £400 for a second offence.
The fine is doubled for each further offence up to a maximum of £6,400.
Individuals found holding an illegal gathering of more than 30 people could be fined £10,000.