The R&B star has struggled to shift tickets for gigs later this year and managers have been forced to try and give seats away.
'It has been a big disappointment,' one source told a US newspaper.
'The ticket sales in big US cities like Boston are so bad, they will barely cover basics like the lighting and other arena costs. Tour managers are begging local radio stations to do giveaways.'
Umbrella star Rihanna, 23, is due to perform at the TD Garden arena in Boston on July 24 with Cee Lo Green as part of the Loud tour. Only 3,700 tickets have been sold so far.
Tour insiders say she needs to sell at least 15,000 to break even.
They expect more than $500,000 USD in losses from the Boston concert alone, the New York Post reports.
The tour begins in June 4 in Baltimore and heads to Canada and then around the US before moving to the UK in August.
A source said: 'She should've been doing smaller venues.
'She's not ready to headline an arena tour.'
A representative for Rihanna was unavailable for comment.