Deuteronomy is originally from the Hebrew Bible. According to Jewish mythology, the book is from the sermons of Moses. Though, it's believed to be much more recent (something like a 1000 years) than the time period where the figure of Moses (or the person(s) he was based on) would have existed. But, even taking Jewish and Christian mythologies at their word, Jesus had nothing to do with that rule. Also, Jesus probably meant for this rule to end for adherents of Christianity.

Mark 7:14-23:
14 Again Jesus called the crowd to him and said, “Listen to me, everyone, and understand this.
15 Nothing outside a person can defile them by going into them. Rather, it is what comes out of a person that defiles them.”
17 After he had left the crowd and entered the house, his disciples asked him about this parable.
18 “Are you so dull?” he asked. “Don’t you see that nothing that enters a person from the outside can defile them?
19 For it doesn’t go into their heart but into their stomach, and then out of the body.” (In saying this, Jesus declared all foods clean.)
20 He went on: “What comes out of a person is what defiles them.
21 For it is from within, out of a person’s heart, that evil thoughts come—sexual immorality, theft, murder,
22 adultery, greed, malice, deceit, lewdness, envy, slander, arrogance and folly.
23 All these evils come from inside and defile a person.”

So, feel free to boil a young goat in its mother's milk. Jesus is A-ok with that.