According to the The Sun, police were called to the property the ex-EastEnders star shares with Adam Cottrell.
The 31-year-old, who is said to have smashed furniture during the row on Sunday night, is thought to have been charged with two counts of assault and criminal damage.
Cassidy and Cottrell welcomed their first child, baby girl Eliza Beatrice, last October.
The couple, who met at the Isle of Wight music festival in 2009, became engaged last year during a trip to Italy.
Discussing her relationship with Cottrell, Cassidy recently told a magazine: "We are having more sex than ever. But we're not at it like rabbits."
Hertfordshire police said: "A man has been charged with two counts of assault by beating and two counts of criminal damage.
"He will appear at East Herts Magistrates' Court on May 31. We will not be commenting further."
> Natalie Cassidy: 'I've lost weight healthily'