Greater Manchester Police (GMP) called the attack at the cemetery in Rochdale Road, Blackley, "sickening and cruel".
GMP said the boys were arrested on Friday on suspicion of committing a racially-aggravated public order offence.
The boys were released on police bail until 25 July.
In addition to the slogans and graffiti, about 40 headstones were toppled.
Two 13-year-old boys have been arrested after anti-Semitic graffiti and swastikas were daubed over gravestones in a Jewish cemetery in Manchester.