According to Tresa Baldas of the Detroit Free Press, Rodriguez had been seeking $100,000 per month from the two-time American League MVP.
Rodriguez is eligible to continue pushing for more since the current award is temporary.
Rodriguez sued Cabrera last year for more than the $12,000 per month he was paying to support their five-year-old son and two-year-old daughter.
As part of the judge's decision, Cabrera will pay exactly $12,247 per month along with money toward "private schooling, day care, health insurance and extracurricular activities."
Additionally, Cabrera will provide the children with yearly passes to Disney World, Universal Studios and Sea World.
The 34-year-old Cabrera has been married to his wife, Rosangel, since 2002. They have two daughters and one son together.
Cabrera's wife filed for divorce last year after finding out about the affair but later changed her mind, per Baldas.
As part of Rodriguez's continued pursuit of additional child support, Cabrera will be forced to disclose how much he spends on his wife and the three children he has with her.