A Met Police spokesman said the 24-year-old and a man aged 35 – arrested on suspicion of the same offence – had been bailed to a date in July, and that two residential properties had been searched as part of their investigation.
Their arrests on Tuesday came a day after police confirmed they had “received information concerning the alleged supply of illegal drugs at a central London location”.
That followed a report in a tabloid newspaper suggesting Contostavlos acted as a go-between by introducing a journalist to an alleged supplier.
The Sun On Sunday claimed half an ounce of cocaine changed hands following a deal that took place at London’s Dorchester Hotel.
A spokesman for Contostavlos declined to comment on her arrest.
The singer, who found fame with the band N-Dubz, was recently dropped as a judge on The X Factor after two series.
Confirming the decision on Twitter, she wrote: “Just wanted to let you all know that I won’t be part of the X Factor panel this year.
“I’ve had a great time on the show, but this year it’s time to do something different.
“I’d like to thank everyone on The X Factor for two amazing years. Stay tuned as I have a very exciting announcement soon.”
Contostavlos scored a number one hit with her debut single Young in 2012, as well as three top 10 singles during her time in N-Dubz.
Last year, she won an apology from her ex-boyfriend after he leaked footage on to the internet of the two of them performing a sex act.