A translation of the text accompanying her Facebook post read: "Eat before you take a plane with the Royal Air Maroc... as you will risk hungry or end up in hospital".
The footage was uploaded on Saturday.
The Mirror reported that the airline had responded and said the incident would be taken "very seriously" and it would "initiate an investigation".
"We do not know when this video was taken or inside which aircraft," a spokesman said.
"We need to go back through the entire supply chain from our providers to understand [what happened]."
He said the airline had never received complaints about cockroaches before.
British Airways fumigated two planes in 2011 after an infestation of bed bugs on a Los Angeles to London flight.
New Zealand is one of 16 countries requiring "disinsection" on all inbound flights, sometimes using aerosol sprays.
- nzherald.co.nz