The risen Jesus in Luke 24 explains to the disciples on the road to Emmaus that the sufferings of the Messiah are all foretold in the Old Testament (24: 26-7), and this motif is repeated in Acts (Acts 3:18; 17:3; 26:23).
It is in fact not easy to find much about a ‘messianic’ figure explicitly in the Old Testament anywhere; but there is certainly nothing about a suffering messianic figure. (Appeals to the description of the suffering servant figure in Isaiah 53 are not relevant here: the figure of Isaiah 53 is not said to be a messianic figure).
The claim that ‘the Messiah must suffer’ seems to be a Lukan innovation, at least insofar as it makes the explicit claim that suffering is predicted of ‘the Messiah’ in Jewish scripture.
From: Christology and the New Testament: Jesus and His Earliest Followers by Christopher Tuckett, page 142. Tuckett is Professor of New Testament Studies at Oxford University.