I had the same question a while ago, and so I have written up a complete example of animating using a spritesheet as the texture for a PlaneGeometry, and then updating the texture at regular intervals -- check out the example at

http://stemkoski.github.io/Three.js/Texture-Animation.html

and view the commented source code for additional explanation.

Update (2021):

Here is an updated version of the function I recommend using. It fixes the issue with the incorrect tile display order, it automatically updates the next frame, and it returns an object you can use to stop and re-start the animation as desired.

function TextureAnimator(texture, tilesHoriz, tilesVert, tileDispDuration) 

{ 

  let obj = {};



  obj.texture = texture;

  obj.tilesHorizontal = tilesHoriz;

  obj.tilesVertical = tilesVert;

  obj.tileDisplayDuration = tileDispDuration;



  obj.numberOfTiles = tilesHoriz * tilesVert;



  obj.texture.wrapS = THREE.RepeatWrapping;   

  obj.texture.wrapT = THREE.RepeatWrapping;   

  obj.texture.repeat.set( 1/tilesHoriz, 1/tilesVert );

  obj.currentTile = 0;



  obj.nextFrame = function()

  {

    obj.currentTile++;

    if (obj.currentTile == obj.numberOfTiles)

      obj.currentTile = 0;



    let currentColumn = obj.currentTile % obj.tilesHorizontal;

    obj.texture.offset.x = currentColumn / obj.tilesHorizontal;



    let currentRow = Math.floor( obj.currentTile / obj.tilesHorizontal );

    obj.texture.offset.y = obj.tilesVertical - currentRow / obj.tilesVertical;

  }



  obj.start = function()

  { obj.intervalID = setInterval(obj.nextFrame, obj.tileDisplayDuration); }



  obj.stop = function()

  { clearInterval(obj.intervalID); }



  obj.start();

  return obj;

}