The Cwm cueman conquered the Crucible for the third time in May, beating John Higgins 18-16 in an epic final. It was his first world title since 2003. Williams has also won the German Masters and Yushan World Open this year and climbed to second place in the world rankings.
Footballer Gareth Bale, cyclists Elinor Barker and Geraint Thomas, Winter Olympian skeleton athlete Laura Deas and Paralympic skier Menna Fitzpatrick also make the shortlist.
The award is given to the person whom, it is felt, has achieved most in Welsh sport over the past year.
The winner will be revealed during an awards show at the Celtic Manor Resort, Newport, on Tuesday, 4 December 2018 after a public vote.
You will be able to vote by telephone or online for the nominee of your choice. Voting will open at 08:00 GMT on Monday, 26 November and will close on 18:00 GMT on Sunday, 2 December.
Rugby union player Jonathan Davies took the award last year and the list of previous winners includes Welsh sporting greats such as footballer Ryan Giggs, boxer Joe Calzaghe and Paralympian Tanni Grey-Thompson.
Rhodri Talfan Davies, director of BBC Wales, said: “The unveiling of the BBC Cymru Wales Sports Personality of the Year is the highlight of the Wales Sport Awards, and an important opportunity for us to thank the people who have entertained and inspired us throughout the year.
“This is a rich shortlist and is reflective of an exceptional year of Welsh sport across a number of fields and I look forward to seeing the winner crowned next month.”
Voting for BBC Cymru Wales Sports Personality of the Year 2018 will open from 08:00 GMT on Monday, 26 November and close at 18:00 GMT on Sunday, 2 December.
Full voting terms and conditions will be available on the BBC website and will also be carried on radio and television.
The winner will be unveiled on Tuesday, 4 December.
This event is not connected with the UK Sports Personality of the Year and is for the Wales award only.