Around 70 people were at the event at the Soho Foundry Tavern in Smethwick last Sunday, and three – including some staff – have since tested positive for Covid-19, council officials say.
The pub closed voluntarily on Thursday after the cases became known.
Experts have warned pubs create the “perfect storm” for spreading coronavirus and carry more risk of infecting others than planes.
They say the most common method of transmission in the UK is probably through conversations.
Public Health England bosses have issued an “urgent appeal” to anyone who attended the barbecue to self-isolate as they may have been exposed to the virus.
Deputy council leader Maria Crompton said: “We urgently need to alert anyone who attended the event last weekend to self-isolate until Sunday 16 August. If they have any symptoms they should book a test.
“Everyone needs to stay incredibly vigilant – the virus is still out there, and the situation remains extremely serious, as this potential outbreak shows.”
She urged employers of those who need to self-isolate to be supportive.
“Pubs need to be very careful at this time to gather contact details of customers and ensure social distancing at all times.”
The Local Government Association has called for councils to have greater powers to close pubs to slow the spread of the virus.
The borough of Sandwell, which includes Smethwick, was in the top 10 areas of England with the highest rates of infections earlier this month.
Ten days ago, a branch of McDonald’s in Smethwick closed after five members of staff tested positive.
But the number of new cases in the borough dropped by 30 per cent in the past week.