The thing you want to instantiate is null & the variable nextTetrimino is assigned but its value is never used.

public static int gridWidth =10; public static int gridHeight =20;

 // Use this for initialization
 void Start () {

     SpawnNextTetrimino();
 
 }
 
 // Update is called once per frame
 void Update () {
 
 }

 public void SpawnNextTetrimino()
 {
     GameObject nextTetrimino = (GameObject) Instantiate (Resources.Load(GetRandomTetrimino(), typeof(GameObject)), new Vector2(5.0f, 20.0f), Quaternion.identity);
     

 } 

 public bool CheckIsInsideGrid (Vector2 pos){
     return ((int)pos.x >= 0 && (int)pos.x < gridWidth && (int)pos.y >= 0);
 }

 public Vector2 Round (Vector2 pos){
     return new Vector2 (Mathf.Round (pos.x), Mathf.Round (pos.y));
 
 }

 string GetRandomTetrimino()
 {

     int randomTetrimino = Random.Range(1, 8);

     string randomTetriminoName = "Prefabs/Tetromino_T";

     switch (randomTetrimino)
     {
         case 1:
             randomTetriminoName = "Prefabs/Tetromino_T";
             break;
         case 2:
             randomTetriminoName = "Prefabs/Tetromino_Long";
             break;
         case 3:
             randomTetriminoName = "Prefabs/Tetrimino_Square";
             break;
         case 4:
             randomTetriminoName = "Prefabs/Tetrimino_J";
             break;
         case 5:
             randomTetriminoName = "Prefabs/Tetrimino_S";
             break;
         case 6:
             randomTetriminoName = "Prefabs/Tetrimino_Z";
             break;
         case 7:
             randomTetriminoName = "Prefabs/Tetomino_L";
             break;

     }

     return randomTetriminoName;
 

 }
   

}