In an item for the comedian's Radio 2 show last week, Brand and guest Jonathan Ross recorded messages about Sachs's granddaughter.
In one recording, Ross was heard shouting "he f**ked your granddaughter" as Brand was leaving a message.
Brand sang in another: "I said some things I didn't of oughta, like I had sex with your granddaughter, though it was consensual. It was lovely sex. It was full of respect."
Sachs's agent Meg Pool revealed that the stunt had upset 78-year-old Sachs, who played Spanish waiter Manuel in the classic BBC sitcom.
Brand apologised on his show on Saturday night, telling listeners: "Sometimes you mustn't swear on someone's answer phone."