A change to a low carb diet might sometimes make that you get low on some of the important vitamins. It might be hard to get a natural intake of these vitamins without eating fruit. So there might be a reason to look into if you need to take vitamin supplements.
It might however be that if your diet consists of meat, fish and eggs and in addition some vegetables this might be all that you actually need. There might be no need to take any additional vitamins.
It however could be good to consider to eat some vitamin D supplements which is essential for health. This is however not only for people who eat according to a low carb diet. Additional D vitamin intake applies for most people no matter what diet you eat according to.
That you need to eat fruit to get enough vitamins is a myth. One example is vitamin C where orange is far down the list of foods with the highest vitamin C content of 51 mg of vitamin C per 100 grams of orange. This compares with eg broccoli has 120 mg C-vitamin/100 gram and yellow peppers with 204 mg C-vitamin/100 grams.
Vitamin A (Retinol): Liver, eggs, butter, milk
Vitamin B1 (Thiamine): meat (pork and beef), Sunflower seeds, sesame seeds
Vitamin B2 (Riboflavin): Meat, liver, kidney, almonds
Vitamin B3 (Niacin): meat, liver, fish, milk
Vitamin B5 (Pantothenic Acid): Avocado, nuts
Vitamin B6 (pyridoxine): Liver, Meat, Fish, Nuts
Vitamin B8 (Biotin): Eggs, liver
Vitamin B12 (cobalamin): meat, liver, herring
Folate / Folic Acid: Liver, Asparagus, Eggs, Broccoli, Cauliflower
Vitamin C (Ascorbic Acid): Peppers, Broccoli, Cauliflower
Vitamin D (Kaciferol): Oily fish, eggs, liver, butter
Vitamin E (alpha-tocopherol): Almond, Spinach, Egg
Vitamin K (phylloquinone): Lettuce, Spinach, Broccoli, liver
It is possible to get your full need of Vitamins from these different low carb food sources. However if you do not alternate your food we recommend you to purchase some vitamin supplements to ensure you get your needed dose. Remember that getting enough vitamins is essential to have your body function in a proper way.