Smith – who took charge in June, 2015 – resigned on Tuesday morning, two days after a 42-28 home defeat by Catalans Dragons.
The 61-year-old Australian was a surprise appointment following James Webster’s departure last year and helped keep Wildcats in Super League.
They finished bottom of the table after the regular rounds and were fourth in the middle-eights, but a win over Bradford Bulls in the one-off million pound match preserved their top-flight status.
Wildcats are currently third from bottom, with one win – away to Hull KR – and four defeats.
Smith gave no hint about a possible exit in his press conference following the Catalans defeat, when he admitted he was disappointed with Wildcats’ defensive effort.
The Belle Vue outfit trailed 26-0 after 27 minutes, but cut the gap to four points before Catalans pulled clear in the final quarter.
Wildcats are due to hold their weekly press briefing – ahead of Friday’s trip to St Helens – on Wednesday, when the coach’s exit is likely to be officially confirmed.
Despite no significant improvement in results, players have hailed Smith for improving team organisation and professionalism.
Smith is the second Super League coach to leave his position this season.
Chris Chester, who lives in Wakefield, was axed after Hull KR’s defeat to Wildcats. Ex-Wakefield player Willie Poching had two games in charge before Webster was appointed team boss until the end of the season.