"I have properly analysed the arguments for and against and I have decided not to accept this proposal," Klaus Iohannis told reporters in a televised statement.
"I call on the PSD coalition to make another proposal," he said. He gave no reasons for his rejection of Shhaideh, who is from Romania's small Turkish minority.
The PSD had put forward Shhaideh, 52, after its thumping election victory on December 11 when it won 45 percent of the vote.
Shhaideh's political experience is limited, having served as development minister for six months before the previous PSD-led government resigned in late 2015.
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This and her personal closeness to Dragnea -- he was a witness at her 2011 wedding to a Syrian businessman -- have stoked opposition accusations that she would merely be a puppet.
The PSD's election triumph came barely a year since anger over a deadly nightclub fire that killed 64 people forced it and prime minister Victor Ponta from office.
The inferno inside the Colectiv club was blamed on corrupt officials turning a blind eye to a lack of fire precautions. Poor medical care exacerbated the death toll.
Brussels has long complained about corruption since Romania's accession to the European Union in 2007 and since the fire the country has been making progress tackling it.
However a return to power by the PSD has raised concerns that progress in this area might slow.
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