2010-11: Tobias Lindberg played for the SDE HF U18 and U16 teams and played for the gold medal Stockholm 1 team in the annual TV-Pucken tournament for high school players in Sweden. Lindberg had 2 assists with 18 penalty minutes in nine U18 games. In eight games for SDE HF's U16 team he scored 3 goals with 9 assists and had 18 penalty minutes. Lindberg scored 3 goals with 4 assists in eight TV-Pucken games.
2011-12: Lindberg moved up to to the Djurgarden club, seeing his first U20 action in the SuperElit league as a 16-year-old, and represented Sweden at the 2012 U17 World Hockey Challenge in Canada. He was scoreless and -1 in his only regular season for Djurgarden's U20 team and was +1 with 1 assist in three playoff games. He played 43 games for Djurgarden's U18 squad, including four playoff contests. Lindberg scored 21 goals with 20 assists and had 62 penalty minutes. In six games at the WHC he had 1 assist with 4 penalty minutes.
2012-13: Lindberg made his pro hockey debut, playing five games for Djurgarden's in Sweden's second league (Allsvenskan). He was an assistant captain for Djurgarden's U20 team and led all scorers in the Allsvenskan U18 playoffs. He had 1 assist with the Djurgarden men's team. In 43 U20 games he scored 9 goals with 13 assists and was -2 with 30 penalty minutes. In the two-game playoff series with Skelleftea he had 2 assists and was +1 with 2 penalty minutes. He scored 9 goals with 12 assists and was +18 with 6 penalty minutes in 14 games for Djurgarden U18 and in nine playoff games scored 4 goals with 10 assists; finishing +8 with 24 penalty minutes. Ranked 99th amongst European skaters in Central Scouting's final rankings, Lindberg was selected by Ottawa in the fourth round (102nd) overall of the 2013 NHL Draft.