SELECT 
  MIN(cscart_product_prices.price) 
FROM 
  cscart_product_prices 
  INNER JOIN cscart_products_categories ON cscart_products_categories.product_id = cscart_product_prices.product_id 
WHERE 
  cscart_products_categories.category_id IN (2643, 2662, 2645, 2644) 
  AND cscart_product_prices.lower_limit = 1 
  AND cscart_product_prices.usergroup_id = 0

Query time 0.00285

JSON explain

{
  "query_block": {
    "select_id": 1,
    "cost_info": {
      "query_cost": "585.45"
    },
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_products_categories",
          "access_type": "range",
          "possible_keys": [
            "PRIMARY",
            "pt"
          ],
          "key": "PRIMARY",
          "used_key_parts": [
            "category_id"
          ],
          "key_length": "3",
          "rows_examined_per_scan": 1062,
          "rows_produced_per_join": 1062,
          "filtered": "100.00",
          "using_index": true,
          "cost_info": {
            "read_cost": "107.55",
            "eval_cost": "106.20",
            "prefix_cost": "213.75",
            "data_read_per_join": "16K"
          },
          "used_columns": [
            "product_id",
            "category_id"
          ],
          "attached_condition": "(`cscart_db`.`cscart_products_categories`.`category_id` in (2643,2662,2645,2644))"
        }
      },
      {
        "table": {
          "table_name": "cscart_product_prices",
          "access_type": "eq_ref",
          "possible_keys": [
            "usergroup",
            "product_id",
            "lower_limit",
            "usergroup_id",
            "idx_product_prices_usergroup_limit"
          ],
          "key": "usergroup",
          "used_key_parts": [
            "product_id",
            "usergroup_id",
            "lower_limit"
          ],
          "key_length": "9",
          "ref": [
            "cscart_db.cscart_products_categories.product_id",
            "const",
            "const"
          ],
          "rows_examined_per_scan": 1,
          "rows_produced_per_join": 1062,
          "filtered": "100.00",
          "cost_info": {
            "read_cost": "265.50",
            "eval_cost": "106.20",
            "prefix_cost": "585.45",
            "data_read_per_join": "24K"
          },
          "used_columns": [
            "product_id",
            "price",
            "lower_limit",
            "usergroup_id"
          ]
        }
      }
    ]
  }
}