Apple introduced the voice-activated assistant technology when launching the iPhone 4S in 2011.
But Cheng Kung University in south Taiwan's Tainan city said the technology infringes two patents held by one of its research teams, both related to speech recognition.
The team is led by Wang Jhing-fa, a professor who specialises in chip designs and neural networks facilitating speech and pattern recognition.
"We filed a lawsuit against Apple at a Federal district court in Texas Friday," Yama Chen, a legal affairs manager at the university, told AFP.
Apple Taiwan was not immediately available for comment.
Earlier this month, Chinese technology firm Shanghai Zhizhen Network Technology Co Ltd filed a similar claim against Apple over Siri.
The company's Xiao i Robot software, patented in 2004, operates in a similar way to Apple's personal assistant and works on the iOS and Android operating systems.
Greater China -- which includes Hong Kong and Taiwan -- has become Apple's fastest-growing region, with revenues second only to the United States.
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