Although you can get calcium from such vegetables as collards, mustard greens, kale, broccoli, bok choy, if you are not already taking a calcium supplement, it would be a good idea to take about 1,000 mg of calcium citrate daily while on the low-iodine diet.here is a quick rundown of what foods to avoid on a low-iodine diet:Iodized salt (non-iodized salt is okay).All dairy products (animals secrete