As trading got under way, sister companies Fiat Chrysler Automobiles (FCA), Ferrari and CNH Industrial saw their shares dip over 4 percent each.
The three groups are controlled by the Agnelli family.
By 10:50 am (0830 GMT), FCA's stock had recovered significantly, edging upwards to a 1.4 percent loss. Ferrari was down 1.8 percent while CNH Industrial lost 2.3 percent.
The losses came after Marchionne stepped down Saturday after 14 years at the helm of Fiat.
The 66-year-old suffered serious complications following surgery on his right shoulder last month and "will not come back to work," according to the Fiat Chrysler group.
The Italian-Canadian executive had taken the reins at Fiat in 2004.
He revamped Fiat, Italy's premier private enterprise, from top to bottom.
In 2009, he merged Fiat with US automaker Chrysler, then hived off its industrial vehicles to create CNH Industrial in 2011 and successfully spun off the luxury brand Ferrari in January 2016.