Two of the detainees were described as journalists who were among the dozens of protesters who took part in the unsanctioned rally at the Monument of Independence in central Almaty.
It was the second such rally this weekend, Russia's RIA Novosti news agency said. Saturday's event led to the detention of another group of protesters.
The crowd's ire was aimed at a decision made by the government last week to devalue the Kazakh tenge by 18.9 percent. RIA Novosti said the move trailed the recent weakening of the Russian ruble, which last month hit its lowest level against the U.S. dollar since 2009.
Some analysts believe the move was made to keep Kazakh oil exports competitive on the world market.