Carrot (Daucus carota L.) is an important root vegetable crop in the Apiaceae and is widely cultivated around the world. Expansins play crucial roles in the growth and development of plants. Here, a total of 35 carrot expansins were identified from carrot. Sequence alignment and phylogenetic analysis revealed that carrot expansins could be classified into four subfamilies, each with similar exon/intron structures and motif compositions, indicating that carrot expansins were relatively conserved during evolution. Chromosomal localization and gene duplication analysis indicated that DcEXP genes were unevenly distributed across carrot nine chromosomes and had evolved predominantly under purifying selection. Measurements of key agronomic characters of carrots at different developmental stages (30, 60, and 90 days after sowing) indicated significant positive correlations among root fresh weight, aboveground fresh weight, root–shoot ratio, root length, and root diameter. The period from 30 to 60 days after sowing was identified as the primary phase of taproot enlargement. Analysis of spatiotemporal expression patterns revealed that most DcEXP genes were specifically expressed in the taproots, and only one gene, DcEXP18, was specifically expressed in leaves. During the rapid growth period of carrot taproots (30 and 60 days after sowing), the genes DcEXP2, DcEXP3, DcEXP5, DcEXP8, DcEXP11, DcEXP13, DcEXP17, DcEXP19, DcEXP20, DcEXP22, DcEXP26, DcEXP28, and DcEXP33 exhibited high expression levels, suggesting that they played potential important roles in carrot taproot enlargement. These findings will advance our knowledge of the molecular mechanisms underlying expansin regulation of carrot growth and development.