The two clubs have also received charges relating to the fracas between both sets of players immediately after Celtic’s 2-1 victory to move 13 points clear at the top of the Scottish Premiership.
Former Liverpool captain Gerrard is understood to have been charged over post-match comments made to referee Bobby Madden and offered a one-match touchline ban.
Brown has been accused of breaching a rule which states players, coaches and officials should “act in the best interests of association football”.
Gerrard accused Brown of antagonising his players and the Rangers support with his celebrations at full-time.
Rangers striker Alfredo Morelos was sent-off for the fifth time this season for elbowing Brown in the first-half and Andy Halliday was also shown a second yellow card after full-time for remonstrating with the Celtic skipper.
Brown was also struck by Ryan Kent following Celtic’s second goal. The Rangers winger faced no action from Madden at the time, but his appeal against a two-match retrospective ban was also dismissed on Thursday.
Regarding a potential ban for Brown, Celtic said in a statement they “will defend these charges vigorously.”
Meanwhile, Celtic have also launched an investigation into a firecracker thrown onto the field during their 2-0 win at St. Mirren on Wednesday.
Buddies goalkeeper Vaclav Hladky had to be treated for a suspected burst eardrum and St. Mirren manager Oran Kearney admitted he considered leading his players off the field.
“Last night’s incident was completely unacceptable and not something we ever want to see repeated. The safety of everyone in football – players, fans, staff, and officials – should always be our priority and, collectively, we need to do all we can to ensure this remains the case,” said Celtic chief executive Peter Lawwell.
“There have a been a number of incidents across many clubs this season, with a range of items, including pyrotechnics, being thrown on to pitches.
“We need to do all we can to remove this from our game.”