The 25-year-old came off the field at the start of the second half and will now undergo surgery. A Cardiff Blues statement said he was likely to be out of action for between three and four months.
Williams, 25, will miss whatever international matches Wales play before Christmas, but hopes to be back in time for the 2021 Six Nations campaign. He played seven times at the Rugby World Cup in Japan last season and now has 20 caps.
“Tomos had been training really well and had hit a bit of form. He was looking forward to going into the Wales camp,” said Cardiff Blues head coach John Mulvihill. “He will get through this and back back even stronger.”