Burnley have apologised for the “unacceptable behaviour” of some of their fans in the win at Sunderland.
Saturday’s match was briefly halted in the first half because missiles were being thrown from the upper tier of the stand housing Burnley supporters.
It is understood an eight-year-old was injured.
The Clarets said an investigation into the incident is ongoing and “anyone caught throwing objects will be liable to a banning order”.
“The club will not let the actions of any individuals spoil, affect, or jeopardise the enjoyment of all our supporters, who have been magnificent all season,” Burnley added.
“We offer our sincere apologies to Sunderland Football Club and to any supporters who may have been affected by this on the weekend.”