Zynga's Bill Jackson said the acquisition was part of a move to expand into new categories of play with "mid-core, multi-platform" games.
A multi-player "Solstice Arena" title being worked on by A Bit Lucky will launch as a Zynga offering.
A Bit Lucky was founded by Frederic Descamps and Jordan Maynard, and the studio's staff of slightly more than 20 people includes veterans of game companies such as Trion Worlds and Xfire.
"After exploring various options and talking to a lot of interested partners, Jordan and I are convinced Zynga is the best choice for us," Descamps said in an email.
"At Zynga we met people like us passionate, hardcore game developers animated by a strong entrepreneurial spirit," he continued. "It was a true meeting of the minds."
Developing richer, more sophisticated games for the array of Internet-connected devices is part of a move by Zynga to be less dependent on Facebook, where it rose to stardom with hits such as "FarmVille" and "Poker."
Zynga recently hired "Mortal Kombat" series co-creator John Tobias to be part of its San Diego studio.
Industry veteran Soren Johnson, who has worked on titles such as "Spore" and "Civilization IV" working on a stealth project in Zynga's studio in Baltimore.
Zynga in March launched its own online playground at zynga.com.
Zynga shares were down three percent at $3.08 at the close of trading Monday on the Nasdaq exchange. Zynga went public in December at $10 per share.