The short answer: there is no strong evidence that collagen supplements are harmful in pregnancy, but there is also no good evidence confirming they are safe. Health authorities like ACOG, the NHS and FDA have not specifically evaluated collagen supplements for pregnant people, and dietary supplements are not tightly regulated. Because of that gap, it is reasonable to be cautious and check with your provider before taking one.
Collagen is the main structural protein in skin, joints and bones. Supplements are usually 'hydrolysed collagen' (collagen peptides) sourced from cows, fish or chicken, sold as powders, capsules or drinks and marketed for skin, hair, nails and joints. Your body already makes collagen from the protein and vitamin C in a normal diet, so a supplement is not a required nutrient the way folic acid or iron are in pregnancy.
Neither ACOG, the NHS, the CDC nor the FDA has issued guidance saying collagen supplements are safe in pregnancy, and there are no good human studies in pregnant people to draw on. The FDA does not review supplements for safety or effectiveness before they are sold, and the NHS notes that supplement quality, dose and added ingredients can vary. With no data showing benefit and none confirming safety, the honest position is 'not proven safe', not 'safe'.
If you are considering collagen, the bigger concern is often what else is in the product: added vitamins (large doses of vitamin A can harm a baby, per the NHS), herbs, sweeteners or heavy-metal contamination that unregulated supplements sometimes carry. Check the full ingredient label with your provider or pharmacist. A well-established alternative is simply eating enough protein plus vitamin C-rich foods, which gives your body what it needs to make its own collagen without an unstudied supplement.