The present invention provides a continuous polymerization apparatus capable of simply and efficiently separating a polymer and solid matter from a reaction mixture while having an apparatus configuration conducive to washing and maintenance, and a continuous production method for a polymer. A continuous polymerization apparatus (100) includes a plurality of reaction vessels (1a to 1c), wherein the plurality of reaction vessels are configured such that reaction mixtures (9a to 9c) successively move through each reaction vessel; in the plurality of reaction vessels, gas phase parts formed above the reaction mixture communicate with one another; and the continuous polymerization apparatus includes a washing part (5), the washing part configured to separate a solid included in the reaction mixture by sedimentation and to perform countercurrent washing.