Officers were called to Ferry Road Drive, Pilton, at about 6.20pm on Sunday afternoon to reports of a domestic row.
They returned to their vehicles parked outside to find them damaged.
Both cars were taken off the road to be repaired.
A Police Scotland spokeswoman said: “Whilst responding to a domestic call in the Ferry Road Drive area of Edinburgh on Sunday 14 October, two police vehicles had their windows smashed.
“Due to the damaged caused, these vital resources had to be removed from operation for repair. Thankfully no one was injured during the incident.
Inquiries are ongoing to trace those responsible and anyone with information is asked to contact Police Scotland via 101, quoting incident number 3381 of 14 October.
Alternatively a report can be made to Crimestoppers via 0800 555 111.
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