Plawecki was born in Hinsdale, Illinois, on February 26, 1991 to Jeff and Lynne Plawecki. He attended Westfield High School in Westfield, Indiana, where he played for the school’s baseball team. He was named an All-State Class 4A honorable mention at catcher in his senior year. He was not selected in the MLB draft following his senior year of high school. He enrolled at Purdue University, to play college baseball for the Purdue Boilermakers baseball team.

As a freshman at Purdue University in 2010, Plawecki had a .343 batting average, a .384 on-base percentage (OBP), and a .529 SLG, with eight home runs. He was named a freshman All-American by Louisville Slugger and the Big Ten Conference (Big Ten) All-Freshman of the Team. Following his freshman season at Purdue, Plawecki played collegiate summer baseball for the Richmond RiverRats of the Prospect League, where he batted 65-for-211 (.308) with fifteen doubles and 27 RBIs.

As a sophomore in 2011, Plawecki batted .341 with a .436 SLG, 2 home runs, and 39 RBIs. He was named first team All-Big Ten. That summer, Plawecki played for the Hyannis Harbor Hawks of the Cape Cod Baseball League.

In the 2012 season as a junior, Plawecki hit .359 batting average, a .445 on-base percentage (OBP), and a .578 SLG, with seven home runs. Plawecki was named the Most Outstanding Player of the 2012 Big Ten Conference Baseball Tournament and 2012 Big Ten Conference Baseball Player of the Year. He was a semifinalist for the Johnny Bench Award in 2011 and one of its three finalists in 2012.

The New York Mets selected Plawecki in the first round, with the 35th overall selection, in the 2012 Major League Baseball draft. In 2013, he played for the Savannah Sand Gnats of the Class A South Atlantic League. He was promoted to the St. Lucie Mets of the Class A-Advanced Florida State League, and to the Binghamton Mets of the Class AA Eastern League for the Eastern League playoffs.

In an April 30, 2017 game against the Washington Nationals at Nationals Park, Plawecki was brought in to pitch for the first time since he was 14 years old. He was the first Mets position player to pitch since Anthony Recker in 2013, also against the Nationals at Nationals Park. He threw only fastballs, giving up four runs over two innings. One of those was Anthony Rendon’s third home run of the game. The Mets lost 23-5.

In 2014, the Mets invited Plawecki to spring training. He started the 2014 season with the Binghamton Mets, where he hit .326 with six home runs and 43 RBIs in 224 at-bats. Plawecki was selected to play for the U.S. Team in the 2014 All-Star Futures Game, along with Noah Syndergaard. After batting .326 for Binghamton, the Mets promoted Plawecki to the Las Vegas 51s of the Class AAA Pacific Coast League on June 24.

The Mets invited Plawecki to spring training in 2015, and reassigned him to minor league camp so that he could start the 2015 season with Las Vegas. After Travis d’Arnaud went on the disabled list with a broken hand on April 19, 2015, the Mets announced they would promote Plawecki to the major leagues.

Plawecki made his Major League debut on April 21, 2015 against the Atlanta Braves. He got his first career hit off Trevor Cahill and finished the game 2-for-4, with two runs scored. During a game against the New York Yankees on April 25, 2015, Plawecki hit his first career home run off CC Sabathia en route to an 8-2 victory. Plawecki became the first player to hit his first career home run in a Mets-Yankees Subway Series game.

Plawecki and his wife, Tayler, were married in November 2015.

Plawecki had surgery on his paranasal sinuses during the 2015-16 offseason to address his dizziness. He batted .197 in 48 games for the Mets in 2016, spending the rest of the season with Las Vegas.

On January 6, 2019, the Mets traded Plawecki to the Cleveland Indians in exchange for Walker Lockett and Sam Haggerty. With the 2019 Indians, Plawecki appeared in 59 games, batting .222 with three home runs and 17 RBIs. He also made two pitching appearances, pitching a total of two innings without allowing a hit, walk, or run. On December 2, 2019, Plawecki was non-tendered and became a free agent.

On January 3, 2020, the Red Sox signed Plawecki to a one-year, $900,000 contract. Overall with the 2020 Red Sox, Plawecki batted .342 with one home run and 17 RBIs in 23 games.