The Hang Seng index fell 1.0 percent, to 28,851.69 points, while the China Enterprises Index lost 1.6 percent, to 11,412.75 points.
A batch of data released on Tuesday showed China's economy cooled further last month, with industrial output, fixed asset investment and retail sales missing expectations as the government extended a crackdown on debt risks and factory pollution.
The top gainers among H-shares were Air China Ltd up 1.18 percent, followed by China Vanke Co Ltd gaining 0.18 percent.
The three biggest H-shares percentage decliners were Byd Co Ltd which has fallen 4.63 percent, New China Life Insurance Co Ltd which has lost 4.4 percent and PetroChina Co Ltd down by 3.1 percent.
China's A-shares were trading at a premium of 30.44 percent over the Hong Kong-listed H-shares.
The sub-index of the Hang Seng index tracking energy shares dipped 2.4 percent while the industrial sector fell 2.1 percent.- Reuters