Twickenham library was closed for three hours last Wednesday morning and the Hampton Hill branch was shut last Friday. Heathfield library had to be closed in March and April.
An angry Councillor Anne Woodward, Conservative spokesman on the leisure services committee, said the problem is a shortage of cash.
She said "The totally inadequate leisure services budget has led to library closures in the past week due to sickness and a shortage of staff."
"I regard it as a scandal that an important committee of this council is expected to operate on such a fragile shoestring."
A spokesman for Richmond Council admitted that the ad hoc closures had been due to staff shortages.
She said: "Whilst we do have some casual staff we can call upon, we do need a minimum number of experienced and fully trained staff who are capable of dealing with the whole range of library issues."
The council claims it will be able to increase staff levels when it reduces the opening hours at five of its branch libraries in July.
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