Vieira, 33, left Whelan in a heap after a shuddering challenge in the first half of the 1-1 draw.
Stoke manager Tony Pulis said referee Alan Wiley did not show "parity" to his team, reduced to 10 men in the second half when skipper Abdoulaye Faye was sent off for a clumsy challenge on Emmanuel Adebayor.
Vieira, who joined City on loan from Inter Milan last month, was making only his fourth appearance for City following his return to England since leaving Arsenal in 2005.
The Frenchman is no stranger to disciplinary action, having been sent off eight times during his nine year career at Arsenal. He has also been dismissed 13 times in total throughout his career.