The answer? Probably the opposite. The foods consumed on a low-carb diet are highly nutritious. For example, eggs (a staple for most people on low carb) may provide the most complete nutrition of any food on the planet.
Consider that a complete chicken can be formed from the nutrients inside the egg. There’s no way for the chicken to pop out and get some vitamins while growing in the egg, everything has to be there. And by eating an egg we get all those nutrients.
Meat, fish and vegetables are also highly nutritious foods. And many people eating low carb tend to replace nutrient-poor pasta, rice and potatoes with more nutrient-rich vegetables.
Compared to that, modern flour is more or less devoid of any nutrition whatsoever apart from pure starch. Usually it’s legally required to add vitamins to flour, so that people who eat a lot of it do not get vitamin deficiencies.
On top of that problem, grains like wheat are high in phytic acid that can reduce absorption of many minerals.
Fruit is often thought to be very nutritious. This is a sad misunderstanding. Apart from vitamin C there are very few nutrients in most modern fruit. These days, they are modified to be very sweet and mostly supply nutrients in the form of sugar. Fruit is basically candy from nature, and should probably be eaten in moderation. Juice is of course even worse.
Modern fast food and junk food also contain a lot of calories and not much nutrition. And low-fat products are low in essential fat-soluble vitamins.
Bottom line: Switching from a standard Western diet to a low-carb diet based on real foods is likely to significantly increase the amount of vitamins and minerals you get from your diet.