Here a solution that handle also the escaping of all UNICODE Control Characters generating a fully valid JSON string (+ the replacement regex is only one):

const chars = {
  "\"": "\\\"",
  "\\": "\\\\",
  "\/": "\\/",
  "\u0000": "\\u0000",
  "\u0001": "\\u0001",
  "\u0002": "\\u0002",
  "\u0003": "\\u0003",
  "\u0004": "\\u0004",
  "\u0005": "\\u0005",
  "\u0006": "\\u0006",
  "\u0007": "\\u0007",
  "\u0008": "\\u0008",
  "\u0009": "\\u0009",
  "\u000A": "\\u000A",
  "\u000B": "\\u000B",
  "\u000C": "\\u000C",
  "\u000D": "\\u000D",
  "\u000E": "\\u000E",
  "\u000F": "\\u000F",
  "\u0010": "\\u0010",
  "\u0011": "\\u0011",
  "\u0012": "\\u0012",
  "\u0013": "\\u0013",
  "\u0014": "\\u0014",
  "\u0015": "\\u0015",
  "\u0016": "\\u0016",
  "\u0017": "\\u0017",
  "\u0018": "\\u0018",
  "\u0019": "\\u0019",
  "\u001A": "\\u001A",
  "\u001B": "\\u001B",
  "\u001C": "\\u001C",
  "\u001D": "\\u001D",
  "\u001E": "\\u001E",
  "\u001F": "\\u001F",
  "\u007F": "\\u007F",
  "\u0080": "\\u0080",
  "\u0081": "\\u0081",
  "\u0082": "\\u0082",
  "\u0083": "\\u0083",
  "\u0084": "\\u0084",
  "\u0085": "\\u0085",
  "\u0086": "\\u0086",
  "\u0087": "\\u0087",
  "\u0088": "\\u0088",
  "\u0089": "\\u0089",
  "\u008A": "\\u008A",
  "\u008B": "\\u008B",
  "\u008C": "\\u008C",
  "\u008D": "\\u008D",
  "\u008E": "\\u008E",
  "\u008F": "\\u008F",
  "\u0090": "\\u0090",
  "\u0091": "\\u0091",
  "\u0092": "\\u0092",
  "\u0093": "\\u0093",
  "\u0094": "\\u0094",
  "\u0095": "\\u0095",
  "\u0096": "\\u0096",
  "\u0097": "\\u0097",
  "\u0098": "\\u0098",
  "\u0099": "\\u0099",
  "\u009A": "\\u009A",
  "\u009B": "\\u009B",
  "\u009C": "\\u009C",
  "\u009D": "\\u009D",
  "\u009E": "\\u009E",
  "\u009F": "\\u009F"
};
export const escapeJsonString = str => str.replace(/[\"\\\/\u0000-\u001F\u007F\u0080-\u009F]/g, match=>chars[match]);

Note that \b \f \n \r \t are not listed as already matched by \u0008 \u000C \u000A \u000D \u0009 respectively.

The proposed code is expected to be in a JS module due to the bulky chars replacement map, but you can also remove the export and add it all in a function if you prefer.