The vast majority - over 980 - relate to Rodrigo Alves.
It follows him receiving a formal and final warning by Big Brother - just one day into the new series.
So-called 'Human Ken Doll' Rodrigo was hauled to the Diary Room in Friday's show for using the 'N word' twice during a conversation with his fellow housemates on launch night.
Big Brother said: "Rodrigo before you entered the Big Brother house the rules regarding unacceptable language and behaviour were explained to you," explaining that his language was "highly offensive" to both viewers and other housemates.
Reacting, Rodrigo said: "Last night I was very excited to be here and I had quite a lot to drink. I was drunk, very drunk. Today I am very hungover and regretting that..."
But Big Brother interrupted: "None of that is relevant. That is not an excuse."
Big Brother continued: "Your language was totally unacceptable and is something Big Brother does not tolerate.
"As a result of your use of this language, Big Brother is giving you a formal and final warning. if you use this language again you will be removed from the house."
Some viewers feel Big Brother didn't go far enough, calling on Rodrigo to be removed from the house as others have been in the past.
Meanwhile, other complaints in the first few days of the series relate to the recent "building a wall" task.
Housemates had to construct a border in the garden and protect it from intruders, a reference to US president Donald Trump's controversial plans for an immigration crackdown at the Mexican border.
A spokesperson for Ofcom said: "We will assess these complaints against our broadcasting code before a decision is made whether to investigate."
Celebrity Big Brother 2018 highlights episode airs nightly on Channel 5.