Fans spilled on to the pitch at the DW Stadium as the hosts celebrated their 1-0 fifth round win against the runaway Premier League leaders.
Supporters from both clubs were involved in disturbances, while television pictures appeared to show a home supporter and striker Aguero involved in a physical exchange.
Advertising hoardings were ripped out and thrown and a pitch invasion by Wigan fans got out of hand while the defeated City players were being escorted off the pitch.
Video footage also appeared to show objects, including an advertising board, being thrown at police officers by fans in the City end.
The match itself was also a fiery affair, with City manager Pep Guardiola and Wigan counterpart Paul Cook involved in a heated confrontation in the wake of Fabian Delph's controversial red card on the stroke of half-time.