Following Smith for the rest of the Pittsburgh series will be Mike Leake on Wednesday and Anthony DeSclafani on Thursday. Cueto will pitch Friday's series opener vs. the Mets at Citi Field, followed by Michael Lorenzen and Smith.
According to a team spokesperson, the change was made to give Cueto a couple of extra days of rest. But it was not specified if he was dealing with a health issue. Cueto missed a start last month after he experienced right elbow stiffness.
The club also revealed that closer Aroldis Chapman is on paternity leave.
In 13 starts combined this season with Louisville, Double-A Pensacola and Class A Dayton, Smith is 4-4 with a 3.04 ERA, 13 walks and 60 strikeouts over 74 innings pitched.
Smith, 27, was a 21st-round selection by the Reds in the 2010 Draft.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, follow him on Twitter @m_sheldon and Facebook and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.