Bully’s, which was AA Restaurant of the Year Wales in 2014-15, tweeted the booking after both a table of two and a table of six failed to show up for dinner service on 21 April.
The post included the name, phone number and email address of one of the diners who had booked.
Bully’s later deleted the tweet and apologised, saying it had been “fuelled by emotion”.
The restaurant’s owner, Russell Bullimore, told WalesOnline he had grown increasingly frustrated with no-shows, which cost the business around £50,000 a year.
“I don’t want to have to start taking money off people before they sit down, I want people to pay for food because it deserves it,” said Bullimore. “I’ll probably have to invest in some way of getting people’s credit card details [for deposits].”
The customer named in the tweet, Emily Quinlan, said on Twitter that she could not attend due to an emergency.
She wrote: “I will be passing this on to the Information Commisioners office. Your complete lack of professionalism and decorum has clearly lost you custom already.
“It was a table for two and I highly doubt you lost £400. Maybe you should reconsider the industry in which you work.”
A number of restaurants have been adopting new methods to discourage no shows.
In March Restaurant Mark Greenaway in Edinburgh began taking credit or debit card details for all bookings, and charging guests who didn't turn up a fee of £30 for lunch and £50 for dinner after it had 450 no shows in one month last year.