Jude Cisse said sons Cassius, 13, and Prince, 11 - both aspiring footballers themselves - were targeted in a string of social media messages.
The abuse was said to include a reference to a match where rival fans hurled bananas at their father, while another message included a racial slur alongside laughing emojis.
Ex-Liverpool striker Cisse had a season-long loan at Sunderland from French club Marseille in 2008-09, when he scored 10 goals in 35 games.
Now 37, he plays for Italian side A.C. Vicenza 1902, while his ex-wife, from whom he was divorced in 2014, still lives in Cheshire.
She told the Sunday Mirror: "The abuse my boys have suffered is beyond belief. What kind of sick individual would target a child like that?
"It has left them talking about the colour of their skin and feeling different."
Describing the messages as "horrendous", she told how she was "utterly horrified" by the online attacks.
But she said she wanted to speak out to send a "clear message that racism and online abuse is not, and will never be, acceptable".
One message to Cassius – who plays for Crewe Alexandra Academy – makes a racial slur alongside three laughing-crying emojis.
Prince – a youth team player at Liverpool – also received a string of shocking messages via Instagram in recent days.
They were sent as Tottenham star Danny Rose went public over his despair at football's inability to tackle racism effectively.
Ms Cisse, 43, says her ex-husband is “absolutely fuming” at the attacks on his boys and is “fully supportive of the ongoing investigation”.
Cheshire Police are said to be investigating whether a racially aggravated public order offence has been committed.